It's a different agreement but the same property and the same RPZ legislation.
Are you making a loss on this property or just want to maximise profits.? If the latter, one needs to be careful as the RPZ legislation is framed/established to protect tenants, keep rents down. Your proposal is not unique or novel.
You posted previously about how the low rent and the RPZ. Honestly, now might be the time to sell the property, especially if in between tenancies. Its very difficult to add the substantial value required to an apartment to allow you increase rents above it's current level.