It depends, does your fiber ISP just have an Ethernet jack going to the modem they gave you, with an ONT (the part that takes in the physical fiber and outputs Ethernet) on the outside of your home or in your building’s telecom room (if you’re in an apartment or condo), or does it have the actual fiber strand entering your unit and passing directly into the modem device?

If it’s the latter, odds are you’ll need to keep their modem (as it serves as the ONT as well), since a lot of fiber ISPs are extremely picky about what connects directly to their optical network. You should be able to put it into bridge mode, connect it with Ethernet, and let whatever router you buy handle things like DHCP. If the former (this is how my fiber setup is), you should be able to connect your own equipment directly, so long as you have things like PPPoE credentials and whatever VLAN tag settings your ISP requires available to put in to the router you purchase.