Extension after initial 6 months Tenancy Agreement

Tenancy Types and Management

I would like to extend a T.A. for a further 6 months with a small percentage increase in the rent.

I was told by a letting agent today not to give them a new Tenancy Agreement but to give them a document saying extension to previous T.A.
Am I able to do this without giving them a new T.A?

If this is correct, do you have a document for this as I can not find it on the download section?

I've also been told if I give a new T.A. you have to re-register the deposit each time plus it's best practice to update the inventory. Is this correct?

Thanks in advance for your help.