Section 21 issuing to evict tenants

[Langanby]

I want to issue section 21 to my tenants to get my property back in January or February next year. My problem is that I am about to let a new tenant into the property, and I can't issue a section 21 in the first 4 months of a shorthold tenancy. I have another tenant who is 3 months into their tenancy so I can issue them the notice at the 4 month mark in the middle of next month. The other tenant is on a rolling contract having finished his shorthold tenancy nearly a year ago, so I don't see any problem with issung them a section 21 at any point. I have read that the contract can have a clause in it that says that the tenant agrees that the 4 month period is not necessary. Is this true? In this case I could effectively give the contract and the section 21 simultaneously. Help gratefully accepted