If there's only one appliance in a rented property then the notification is all that's required, doesn't matter when the current LGSC runs out, as the pipework etc doesn't even actually have to be recorded on the form, although most engineers do a TT and include it on the LGSC, so it's only when the boiler is one year old that a new LGSC will be required
It seems quite a lot,of engineers arent aware of this,
Well you learn something new everyday.
I always fill one out anyway even if not rented just to show that I have checked it etc