Rent rise during periodic & compliance with Tenancy Agreement.

Tenancy Types and Management

My tenants have been in our property for 18 months since Sept '19. The 12 month AST they had then ran into a periodic. The AST agreement was done by the letting agent who found me the tenants. I didn't put the rent up at the 12 month stage due to the pandemic, but I need to be doing so before too long.

I thought I'd have to wait until September '21 due to the wording on the tenancy agreement (below), but talking to the letting agent today I was told that I could do it any time during a periodic.
%7EIs this correct?( I haven't always had correct advice from various other agents!)

The tenancy agreement states:
'It is agreed that the rent as defined in this Agreement will be reviewed in an upward only fashion on the anniversary of this tenancy and upon each subsequent anniversary in line with the RPI increases for the previous 12 moths and subject to a minimum of %C2£5 per calendar month or 5% whichever is greater.'

%7EAlso, the agent told me that if I put the rent up, it is recommended that I renew the tenancy agreement. Is this really necessary?
%7EIf so, what does the contract need to include?