Royal Navy primarily cutting cost (6)
I believe the answer is:
prince
'royal' is the definition.
(prince is a kind of royal)
'navy primarily cutting cost' is the wordplay.
'primarily' says to take the initial letters.
'cutting' is an insertion indicator (some letters cut their way into a word).
'cost' becomes 'price' (the cost or price of something).
The first letter of 'navy' is 'n'.
'n' placed within 'price' is 'PRINCE'.
(Other definitions for prince that I've seen before include "Boxer Naseem Hamed's "title"" , "See 1" , "Royal personage" , "Canadian province" , "Son of a royal house" .)