For service records for persons serving after 1938, you should contact:
Data Protection Cell (Navy), Victory View, Building 1/152, HM Naval Base, Portsmouth, PO1 3PX.
The Ministry of Defence also holds records of deceased Service Personnel, which have not yet been passed on to the National Archives. A search fee of £30 is currently charged for copies of these records, but a Spouse at the time of the deceased’s death can obtain a copy for free.
For full details on how to apply for service records of Royal Navy personnel, visit the Requests for personal data and service records page on the Gov.uk site