An article from White & Case on 23rd February says that, in the event of a “no deal” Brexit, the UK will cease its participation in the European Arrest Warrant (EAW) regime and revert to the 1959 European Convention on Extradition. This is expected to create substantial legal and political hurdles to the continued EU-UK co-operation on extradition. Most notably, Germany has already declared it will stop extraditing its nationals to the UK post-Brexit. It points out that the current extradition regime in the UK is governed by the Extradition Act 2003, where territories with whom the UK shares an extradition relationship are defined as either Part 1 (European Arrest Warrant) or Part 2 (other territories). Published regulations make provision for amending the 2003 Act so that after Brexit all extradition requests to and from EU states will once again be regulated by the 1959 Act.
https://www.jdsupra.com/legalnews/extradition-back-to-the-future-with-no-87392/