Changing one of the tenants before end of tenancy

Tenancy Types and Management

I have a Assured Shorthold Tenancy Agreement Provided under part 1 of the Housing Act 1988 and amended under part 3 of the Housing Act 1996 started on 2 July 2022 . The contract was downloaded from NRLA website in April 2022. The contract was signed by 4 tenants. One of them is willing to end her tenancy and she has already found a replacement for her. I am happy to help the current tenant to move out and allow the new replacement to start. But I am not sure of how proceed as the tenants are under the old contract terms, when the new legislation have been introduced . My Question is , can I switch from old contract to the new contract and change the name of one of the tenants ? and how to proceed from here please.