You don't terminate at first!
You want to re-use your current fibre port assigned to your premise, not letting them go!
If you release your port, chances of getting it back will be low if your area have pending queue to install.

--

Just like mobile MNP; you go to your replacement ISP first to put in transfer "purchase order".
You'll take the reference number generated back to your current ISP, to
let them know and confirm to release current port to replacement ISP.

With both sides acknowledging your switching request, they'll arrange to have your replacement ISP to install first, then days later your old ISP will disconnect after confirm no issue during switch.
Your bill will have short overlap period, which you are liable to pay both.