On the strictly official side of things, Rita is a District Attorney and a Reserve Navy Commander within the JAG Corps, and she gets embroiled in some cases that Pride and his NCIS team are investigating.
Don’t be disappointed when sparks aren’t immediately flying, as the follow-up episode is where the heat starts up.
When Chelsea Field shows up on NCIS: New Orleans, which is set to happen in the March 7 installment, she will be playing Rita Devereaux, an old friend from Pride’s past.
It should not be much of a (non-quantum) leap for him to get along with her on the set, since they should have perfect chemistry.