New property & new tenant

Tenancy Types and Management

Hi
I am buying a flat with a tenant in situ on a periodic tenancy. I want to ensure that I do things correctly both for myself and the tenant, who I want to keep. I have met the tenant and have confirmed the rent is paid up to date.
So can I;
A, get the tenant to sign a new STA between exchange and completion.
B; get the managing agents (who hold the deposit) to transfer the deposit on the day of completion.
C; take a new inventory after completion.
D; check the tenant moved in after 1997.
and then expect to be ok?
Or are there pitfalls I have overlooked?
Thanks