Hi @new.one
Unfortunately the regulations set out by HMRC do not allow for this.
You can only transfer cash in and out of your ISA.
It’s to ensure that people crystallise their realised gains/losses and pay the appropriate taxes prior to topping up their ISA contributions or least that is my understanding.
@Richard.W perhaps we should include this in the tax sticky?
Reference:
You cannot transfer any non-ISA shares you already own into an ISA