The European Arrest Warrant is an EU council framework decision which only applies to and between EU Member States:
- The European arrest warrant is a judicial decision issued by a Member State with a view to the arrest and surrender by another Member State of a requested person, for the purposes of conducting a criminal prosecution or executing a custodial sentence or detention order.
https://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX:32002F0584
The UK is ceasing to be a Member State, and the framework decision has no structure for non-Member States taking part, hence the UK must also leave the EAW community - the UK has made the decision not to try to have this situation altered.
Interestingly enough, the UK's “Future Relationship” document which lays out the intention to leave the EAW (or rather, not to seek continued membership of it), says the following:
The UK is not seeking to participate in the European Arrest Warrant as part of the future relationship. The agreement should instead provide for fast-track extradition arrangements, based on the EU’s Surrender Agreement with Norway and
Iceland which came into force in 2019, but with appropriate further safeguards for individuals beyond those in the European Arrest Warrant.
This leaves some ambiguity, as the EU framework decision has the following line specifically in it:
- This Framework Decision shall apply to Gibraltar
This potentially means that Gibraltar could remain within the EAW community despite never being a member state, as it's explicitly mentioned as included. The UK document makes no mention of Gibraltar either.