Cut and run most of the navy (4)
I believe the answer is:
flee
'cut and run' is the definition.
(I've seen this before)
'most of the navy' is the wordplay.
'most of' means to remove the last letter.
'the navy' becomes 'fleet' (I've seen this before).
'fleet' with its final letter taken off is 'FLEE'.
(Other definitions for flee that I've seen before include "Cut and run" , "rush" , "Do a runner" , "Maybe escape" , "Leave" .)