If I transfer in a Stocks and shares ISA will it count towards my annual ISA allowance?

No, providing you simply transfer the funds directly from one ISA provider to another, it has no bearing on your overall annual ISA subscription allowance for the tax year.

However, if you transfer a Stocks and shares or cash ISA into a Lifetime ISA, while this will not affect your overall annual ISA subscription allowance for that tax year, it will could towards your Lifetime ISA payment limit of £4,000. Transfers into Lifetime ISAs will be available later in the year.