How to use UART interrupts for PIC24 with MCC?
What happens when the interrupts are configured properly the interrupt for your UART needs to be enabled in some register bit(s). Before enabling there is also a need to setup the pointer (address) of the interrupt handler routine. In the simplest case for some MCUs the handler address gets placed into the interrupt vector table which is typically in a dedicated memory location. In more complex cases the MCU has a more generic interrupt vector for some group of interrupt sources. The specific handler addresses for the group of interrupt sources are placed into a table. Later a software routine that responds to the actual group interrupt then figures out what specific source triggered the interrupt and calls the appropriate handler via the correct table entry.

Note that the more complex case I described is really just an adaptation of the simpler case. It is the MCU hardware that takes care of responding to the enabled interrupt source. It correlates the source to a specific interrupt vector table entry and then gets the handler address from the vector and calls to the handler routine.