Will my monthly renewal date change if I change plans?

I’m currently on a monthly SIM-only contract that runs from the 15th to the 14th of the month, but there are better deals available now for the same price I’m paying.

If I upgrade, will the new contract become effective straight away, or will it not commence until the current billing period is over? I’d prefer the latter, since I don’t want to be paying a full month’s fee for just part of a month!

If it does kick in straight away, when would be the best time for me to place the order, in order to minimise the time lost?