hattieB:

Previous year's ISAs are an entirely separate allowance to the current years's allowance.

You need to check what maturity options are set for the one year fixed rate. This will be hidden somewhere in the terms and conditions. Probably, but I can't guarantee it, a variable rate ISA. Important its not another fixed rate unless that is what you want.

Then you need to find a provider which accepts transfers and ask the new provider to make the transfer arrangements. Maybe your existing fixed rate provider has a fixed rate offer to choose.