diff --git a/pallets/aura-ext/Cargo.toml b/pallets/aura-ext/Cargo.toml
index 1db43697511..df145aad522 100644
--- a/pallets/aura-ext/Cargo.toml
+++ b/pallets/aura-ext/Cargo.toml
@@ -18,6 +18,9 @@ sp-consensus-aura = { git = "https://github.com/paritytech/substrate", default-f
 sp-runtime = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 sp-std = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 
+# Cumulus
+cumulus-pallet-parachain-system = { path = "../parachain-system", default-features = false }
+
 [dev-dependencies]
 
 # Cumulus
@@ -35,5 +38,6 @@ std = [
 	"sp-consensus-aura/std",
 	"sp-runtime/std",
 	"sp-std/std",
+	"cumulus-pallet-parachain-system/std",
 ]
 try-runtime = ["frame-support/try-runtime"]
diff --git a/pallets/aura-ext/src/consensus_hook.rs b/pallets/aura-ext/src/consensus_hook.rs
new file mode 100644
index 00000000000..c8806b1f4cb
--- /dev/null
+++ b/pallets/aura-ext/src/consensus_hook.rs
@@ -0,0 +1,56 @@
+// Copyright 2023 Parity Technologies (UK) Ltd.
+// This file is part of Cumulus.
+
+// Cumulus is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+
+// Cumulus is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License
+// along with Cumulus.  If not, see <http://www.gnu.org/licenses/>.
+
+//! The definition of a [`FixedVelocityConsensusHook`] for consensus logic to manage
+//! block velocity.
+//!
+//! The velocity `V` refers to the rate of block processing by the relay chain.
+
+use super::pallet;
+use cumulus_pallet_parachain_system::{
+	consensus_hook::{ConsensusHook, UnincludedSegmentCapacity},
+	relay_state_snapshot::RelayChainStateProof,
+};
+use frame_support::pallet_prelude::*;
+use sp_std::{marker::PhantomData, num::NonZeroU32};
+
+/// A consensus hook for a fixed block processing velocity and unincluded segment capacity.
+pub struct FixedVelocityConsensusHook<T, const V: u32, const C: u32>(PhantomData<T>);
+
+impl<T: pallet::Config, const V: u32, const C: u32> ConsensusHook
+	for FixedVelocityConsensusHook<T, V, C>
+{
+	// Validates the number of authored blocks within the slot with respect to the `V + 1` limit.
+	fn on_state_proof(_state_proof: &RelayChainStateProof) -> (Weight, UnincludedSegmentCapacity) {
+		// Ensure velocity is non-zero.
+		let velocity = V.max(1);
+
+		let authored = pallet::Pallet::<T>::slot_info()
+			.map(|(_slot, authored)| authored)
+			.expect("slot info is inserted on block initialization");
+		if authored > velocity + 1 {
+			panic!("authored blocks limit is reached for the slot")
+		}
+		let weight = T::DbWeight::get().reads(1);
+
+		(
+			weight,
+			NonZeroU32::new(sp_std::cmp::max(C, 1))
+				.expect("1 is the minimum value and non-zero; qed")
+				.into(),
+		)
+	}
+}
diff --git a/pallets/aura-ext/src/lib.rs b/pallets/aura-ext/src/lib.rs
index 15e82edeefe..5605e2f2ac5 100644
--- a/pallets/aura-ext/src/lib.rs
+++ b/pallets/aura-ext/src/lib.rs
@@ -37,9 +37,12 @@
 
 use frame_support::traits::{ExecuteBlock, FindAuthor};
 use sp_application_crypto::RuntimeAppPublic;
-use sp_consensus_aura::digests::CompatibleDigestItem;
+use sp_consensus_aura::{digests::CompatibleDigestItem, Slot};
 use sp_runtime::traits::{Block as BlockT, Header as HeaderT};
 
+pub mod consensus_hook;
+pub use consensus_hook::FixedVelocityConsensusHook;
+
 type Aura<T> = pallet_aura::Pallet<T>;
 
 pub use pallet::*;
@@ -68,6 +71,19 @@ pub mod pallet {
 			// Fetch the authorities once to get them into the storage proof of the PoV.
 			Authorities::<T>::get();
 
+			let new_slot = Aura::<T>::current_slot();
+
+			let (new_slot, authored) = match SlotInfo::<T>::get() {
+				Some((slot, authored)) if slot == new_slot => (slot, authored + 1),
+				Some((slot, _)) if slot < new_slot => (new_slot, 1),
+				Some(..) => {
+					panic!("slot moved backwards")
+				},
+				None => (new_slot, 1),
+			};
+
+			SlotInfo::<T>::put((new_slot, authored));
+
 			T::DbWeight::get().reads_writes(2, 1)
 		}
 	}
@@ -84,6 +100,13 @@ pub mod pallet {
 		ValueQuery,
 	>;
 
+	/// Current slot paired with a number of authored blocks.
+	///
+	/// Updated on each block initialization.
+	#[pallet::storage]
+	#[pallet::getter(fn slot_info)]
+	pub(crate) type SlotInfo<T: Config> = StorageValue<_, (Slot, u32), OptionQuery>;
+
 	#[pallet::genesis_config]
 	#[derive(Default)]
 	pub struct GenesisConfig;
diff --git a/pallets/parachain-system/src/consensus_hook.rs b/pallets/parachain-system/src/consensus_hook.rs
index 8d3606d14b8..bdf590a0fd5 100644
--- a/pallets/parachain-system/src/consensus_hook.rs
+++ b/pallets/parachain-system/src/consensus_hook.rs
@@ -18,6 +18,7 @@
 //! of parachain blocks ready to submit to the relay chain, as well as some basic implementations.
 
 use super::relay_state_snapshot::RelayChainStateProof;
+use frame_support::weights::Weight;
 use sp_std::num::NonZeroU32;
 
 /// The possible capacity of the unincluded segment.
@@ -61,8 +62,8 @@ pub trait ConsensusHook {
 	/// This hook is called partway through the `set_validation_data` inherent in parachain-system.
 	///
 	/// The hook is allowed to panic if customized consensus rules aren't met and is required
-	/// to return a maximum capacity for the unincluded segment.
-	fn on_state_proof(state_proof: &RelayChainStateProof) -> UnincludedSegmentCapacity;
+	/// to return a maximum capacity for the unincluded segment with weight consumed.
+	fn on_state_proof(state_proof: &RelayChainStateProof) -> (Weight, UnincludedSegmentCapacity);
 }
 
 /// A special consensus hook for handling the migration to asynchronous backing gracefully,
@@ -75,8 +76,11 @@ pub trait ConsensusHook {
 pub struct ExpectParentIncluded;
 
 impl ConsensusHook for ExpectParentIncluded {
-	fn on_state_proof(_state_proof: &RelayChainStateProof) -> UnincludedSegmentCapacity {
-		UnincludedSegmentCapacity(UnincludedSegmentCapacityInner::ExpectParentIncluded)
+	fn on_state_proof(_state_proof: &RelayChainStateProof) -> (Weight, UnincludedSegmentCapacity) {
+		(
+			Weight::zero(),
+			UnincludedSegmentCapacity(UnincludedSegmentCapacityInner::ExpectParentIncluded),
+		)
 	}
 }
 
@@ -88,10 +92,13 @@ impl ConsensusHook for ExpectParentIncluded {
 pub struct FixedCapacityUnincludedSegment<const N: u32>;
 
 impl<const N: u32> ConsensusHook for FixedCapacityUnincludedSegment<N> {
-	fn on_state_proof(_state_proof: &RelayChainStateProof) -> UnincludedSegmentCapacity {
-		NonZeroU32::new(sp_std::cmp::max(N, 1))
-			.expect("1 is the minimum value and non-zero; qed")
-			.into()
+	fn on_state_proof(_state_proof: &RelayChainStateProof) -> (Weight, UnincludedSegmentCapacity) {
+		(
+			Weight::zero(),
+			NonZeroU32::new(sp_std::cmp::max(N, 1))
+				.expect("1 is the minimum value and non-zero; qed")
+				.into(),
+		)
 	}
 }
 
diff --git a/pallets/parachain-system/src/lib.rs b/pallets/parachain-system/src/lib.rs
index 50df5e8ba59..5601bcdd17d 100644
--- a/pallets/parachain-system/src/lib.rs
+++ b/pallets/parachain-system/src/lib.rs
@@ -58,12 +58,12 @@ use sp_std::{cmp, collections::btree_map::BTreeMap, prelude::*};
 use xcm::latest::XcmHash;
 
 mod migration;
-mod relay_state_snapshot;
 #[cfg(test)]
 mod tests;
 mod unincluded_segment;
 
 pub mod consensus_hook;
+pub mod relay_state_snapshot;
 #[macro_use]
 pub mod validate_block;
 
@@ -484,7 +484,8 @@ pub mod pallet {
 			.expect("Invalid relay chain state proof");
 
 			// Update the desired maximum capacity according to the consensus hook.
-			let capacity = T::ConsensusHook::on_state_proof(&relay_state_proof);
+			let (consensus_hook_weight, capacity) =
+				T::ConsensusHook::on_state_proof(&relay_state_proof);
 
 			// initialization logic: we know that this runs exactly once every block,
 			// which means we can put the initialization logic here to remove the
@@ -543,7 +544,7 @@ pub mod pallet {
 			// ancestor was included, the MQC heads wouldn't match and the block would be invalid.
 			//
 			// <https://github.com/paritytech/cumulus/issues/2472>
-			let mut total_weight = Weight::zero();
+			let mut total_weight = consensus_hook_weight;
 			total_weight += Self::process_inbound_downward_messages(
 				relevant_messaging_state.dmq_mqc_head,
 				downward_messages,
diff --git a/pallets/parachain-system/src/relay_state_snapshot.rs b/pallets/parachain-system/src/relay_state_snapshot.rs
index 9da5a03ce83..ead077f527d 100644
--- a/pallets/parachain-system/src/relay_state_snapshot.rs
+++ b/pallets/parachain-system/src/relay_state_snapshot.rs
@@ -14,6 +14,8 @@
 // You should have received a copy of the GNU General Public License
 // along with Cumulus.  If not, see <http://www.gnu.org/licenses/>.
 
+//! Relay chain state proof provides means for accessing part of relay chain storage for reads.
+
 use codec::{Decode, Encode};
 use cumulus_primitives_core::{
 	relay_chain, AbridgedHostConfiguration, AbridgedHrmpChannel, ParaId,
diff --git a/pallets/parachain-system/src/tests.rs b/pallets/parachain-system/src/tests.rs
index e1010f89be0..574ab43078d 100755
--- a/pallets/parachain-system/src/tests.rs
+++ b/pallets/parachain-system/src/tests.rs
@@ -121,14 +121,14 @@ std::thread_local! {
 	static HANDLED_DMP_MESSAGES: RefCell<Vec<(relay_chain::BlockNumber, Vec<u8>)>> = RefCell::new(Vec::new());
 	static HANDLED_XCMP_MESSAGES: RefCell<Vec<(ParaId, relay_chain::BlockNumber, Vec<u8>)>> = RefCell::new(Vec::new());
 	static SENT_MESSAGES: RefCell<Vec<(ParaId, Vec<u8>)>> = RefCell::new(Vec::new());
-	static CONSENSUS_HOOK: RefCell<Box<dyn Fn(&RelayChainStateProof) -> UnincludedSegmentCapacity>>
-		= RefCell::new(Box::new(|_| NonZeroU32::new(1).unwrap().into()));
+	static CONSENSUS_HOOK: RefCell<Box<dyn Fn(&RelayChainStateProof) -> (Weight, UnincludedSegmentCapacity)>>
+		= RefCell::new(Box::new(|_| (Weight::zero(), NonZeroU32::new(1).unwrap().into())));
 }
 
 pub struct TestConsensusHook;
 
 impl ConsensusHook for TestConsensusHook {
-	fn on_state_proof(s: &RelayChainStateProof) -> UnincludedSegmentCapacity {
+	fn on_state_proof(s: &RelayChainStateProof) -> (Weight, UnincludedSegmentCapacity) {
 		CONSENSUS_HOOK.with(|f| f.borrow_mut()(s))
 	}
 }
@@ -440,7 +440,9 @@ fn block_tests_run_on_drop() {
 
 #[test]
 fn unincluded_segment_works() {
-	CONSENSUS_HOOK.with(|c| *c.borrow_mut() = Box::new(|_| NonZeroU32::new(10).unwrap().into()));
+	CONSENSUS_HOOK.with(|c| {
+		*c.borrow_mut() = Box::new(|_| (Weight::zero(), NonZeroU32::new(10).unwrap().into()))
+	});
 
 	BlockTests::new()
 		.with_inclusion_delay(1)
@@ -475,7 +477,9 @@ fn unincluded_segment_works() {
 #[test]
 #[should_panic = "no space left for the block in the unincluded segment"]
 fn unincluded_segment_is_limited() {
-	CONSENSUS_HOOK.with(|c| *c.borrow_mut() = Box::new(|_| NonZeroU32::new(1).unwrap().into()));
+	CONSENSUS_HOOK.with(|c| {
+		*c.borrow_mut() = Box::new(|_| (Weight::zero(), NonZeroU32::new(1).unwrap().into()))
+	});
 
 	BlockTests::new()
 		.with_inclusion_delay(2)