Although we have seen changes since 2006, the Royal Wedding in April 2011 and some promotions notably HRH The Duke of Edinburgh to Lord High Admiral, HM The Queen in that year appointed members of the Royal Family to be patrons to various naval commands in recognition of the strong links between the Royal Navy and the Royal Family.

According to the current Royal website [Feb/12] that position has not changed [HRH The Princess of Cambridge has not been included in the list] so the Patrons remain as appointed: I remember this day well, when the Royal Family web site published these family jobs.

They are:-

HRH The Prince of Wales - Admiral - Commodore-in-Chief Plymouth

HRH Prince William -  Flight Lieutenant RAF - Commodore-in-Chief Scotland and Commodore-in-Chief Submarines

HRH Prince Harry -  Lieutenant Household Cavalry [Blues and Royals] - Commodore-in-Chief Small Ships and Diving

HRH The Duchess of Cornwall - Commodore-in-Chief Naval Medical Services and Commodore-in-Chief Naval Chaplaincy Services

HRH The Duke of York - Rear Admiral - Commodore-in-Chief Fleet Air Arm

HRH The Earl of Wessex - Commodore-in-Chief Royal Fleet Auxiliary

HRH The Princess Royal - Vice Admiral and Chief Commandant for Women in the Royal Navy - Commodore-in-Chief Portsmouth

HRH Prince Michael of Kent - Commodore-in-Chief Maritime Services

Note -  Since writing the page, Prince Charles has been promoted to an Admiral of the Fleet.
Princess Anne's husband, Timothy Lawrence is a Vice Admiral, 

Now I am writing this in August 2020  and despite the terrible upheaval caused by the Sussexes disappearing off screen possibly for good and the fall from grace of the Duke of York [no longer, as the song says, "THE FAMOUS"] there must be Royal Patronages for the Navy and Marine gapped with no available taker. And yet all seem the same as originally issued by the Palace and their titles 'by choice' indicator shows what was shown before the bust ups.

 In this case, and as at August 2020 the Royals are appointed the following Patrons and Commodores-in-Chief to the Royal Navy roles.

1.    Her Majesty The Queen -  Patron of the R.N. Cricket Club, Patron of the R.N. Football  Association, Patron of the R.N. Rugby Union, Patron of the R.N. Officers Association. Patron The VC and GC Association.

2.    HRH The Duke of Edinburgh - Patron of the National Museum of the R.N. formerly the Royal Marines Museum, Admiral-in-Chief R.N. Sailing Association.

3.    HRH The Prince of Wales - Patron of the R.N. and R.M. Equestrian Association, Patron of the R.N.Club of 1765 and 1785, Commodore-in-Chief R.N. Plymouth Command, Patron Britannia Association, Patron The British  Forces Association, Patron The Chatham Historic Dockyard Trust, Patron The Fairey Gannet AEW3 Restoration Project, Hon President HMS Hermione Association, Patron HMS Jupiter Association, Patron The Portsmouth Royal Maritime Club, Patron RNBT, Patron The South Atlantic Medal Association SAMA 82, Patron The RNVR and RNR [London Division] Old Hands Association, Patron The Ton Class Association, Patron The White Ensign Association,  Patron The War Widows Association of Great Britain, President of the VC and GC Association,

4.   HRH The Duchess of Cornwall - Sponsor HM S/M Astute, Sponsor HMS Prince of Wales, Commodore-in-Chief Naval Chaplaincy Service, Patron The RBL Poppy Factory,  Commodore-in-Chief R.N. Medical Service,  Patron-in-Chief The [Victory] Association. Patron T.S. Astute [attached to HM S/M Astute].

5.    HRH The Princess Anne The Princess Royal  - Joint Patron of the National Museum of the R.N. formerly the Royal Marines Museum, Patron of the Battle of the Atlantic Memorial, Sponsor HMS Albion, Sponsor HMS Talent, Patron Hornet Services Sailing Club, Vice Patron to the Women of WW2 Memorial, Commodore-in-Chief Portsmouth Naval Command, President Royal British Legion Women's Section, Patron R.N. Equestrian Associatiion Eventing,  Patron Special Boat Sailing Association, Patron Special Forces Club, Patron Association of WREN's, Patron The Naval Ladies Club, Patron The RN and RM Charity, Admiral Chief Commandant Women in the Royal Navy, Patron Women's Benevolent  [WRNS Benevolent  Trust].

6.    HRH The Duke of York - Naval Children's Charity formerly The R.N.and R.M. Childrens Fund. Patron R,N, Golf Association, Patron R.N. Golfing  Society. Patron F.A.A. Museum, Commodore-in-Chief F.A.A. HMS Duke of York Association Hon President, Patron Fly Navy Heritage Trust, Patron Falklands Island Memorial Chapel Trust,

7.    HRH Earl of Wessex - Commodore-in-Chief R.F.A. Service, Patron R.F.A Association.

8.    HRH The Countess of Wessex -  Sponsor HMS Daring

9.    HRH The Duke of Cambridge - Commodore Scotland R.N. Command. Commodore-in-Chief Submarines.

10.  The Duke of Essex - Captain General Royal Marines. Commodore Small ships and Diving.

11,  HRH Princess Alexandra - Sponsor HMS Kent,  Patron The Queen Alexandra's Royal Naval Nursing Service[QARNNS].

Personally I think the choices of No 9 and 10 [second listed appointment]are well chosen and befitting of the Dukes holding in relative terms from the mighty to the minnow appointments!  Sums them up in one really,