You're RDO will ask one local league ref secretary to assign you and every other new ref games. It'll all depend on the number of refs your league now has, which was actually plentiful when I first passed the course due to the very high number of applicants (I think most gave up within a few months).
My advice from my experience is to contact other local league's and tell them that you are a new ref etc and available if required. I got far more games doing that than I did through my RDO, who had more refs than games.
Good luck, be proactive