This airport doesn't have an airside pedestrian access, nor airside buses or trams. All transfers between terminals are accomplished by exiting the terminal and taking shuttle buses that run regularly around the airport from one terminal to the next.
EDIT 1-17-21: Michael Hampton's Answer of January 23, 2020, indicates that there is an airside corridor between T3 and T4.
Assuming your first flight has departure from a US airport, whether you'll go through security again at Ft. Lauderdale will depend on what airline(s) you're on, and whether your flights arrive and depart from the same Ft. Lauderdale airport terminal. If you edit your question to provide airline and flight information, a more specific answer can be provided.
TL;DR: If you have to change terminals in Ft. Lauderdale to reach your ongoing flight to Cancun, you'll exit the arriving flight's terminal, shuttle to the departing flight's terminal, then have to go through security again to reach the departing flight.