What happens when one tenant in a shared property changes?

Tenancy Types and Management

We have a property, let to 3 girls on a single AST, which they all signed. Now one girl is leaving, and the other 2 have found someone else to move in, which we are fine with. The question is, can we just cross out the girl who's leaving, and add the new girl's name and signature to the AST? Does this mean the AST just carries on (it's outside the 6 month initial period), or do we have to start a new AST for all 3 tenants? The tenant who's leaving is the "lead tenant", so her name appears several times on the tenancy agreement - is it OK to change this?

Thanks

Mark Wood