As I have not sailed on Explorer, I had a look at the P&O website (the process is slightly different on Encounter and Adventure):
If you are travelling on Pacific Explorer, you can make specialty dining reservations in Cruise Control. Once onboard, you will be able to book our complimentary restaurants, Waterfront, Angelo's and Dragon Lady, by visiting the booking desk on Deck 6, calling 4800 or through the P&O Cruises App.
Hope this helps and wishing you a great cruise.