Thanks
I should have done a bit more research before asking the question. I found the following on the Regent website.
Dining reservations may be reserved online beginning 75 days before your cruise sails, or 90 days for guests eligible for our Concierge Amenities, at 8pm Eastern US Time. To do so, please create an account via the My Account section of our website and access the Dining Reservations link for your cruise via your Booked Cruises. Guests may pre-book one dinner reservation in each specialty restaurant prior to sailing, then subsequent reservations may be made on board, space dependent. Multiple pre-booked reservations in each restaurant are permitted only on Grand Voyages, with one reservation allotted per voyage segment. Guests may contact the Maître D' once onboard to request additional reservations, if available. Compass Rose and Sette Mari At La Veranda do not require reservations.