Her majesty's personal units? (4)
I believe the answer is:
ones
'units?' is the definition.
('one' can be a synonym of 'unit')
I can't explain the remainder of the clue.
(Other definitions for ones that I've seen before include "Units" , "Aces" , "1 & 1 & 1" , "(Of ship) returning to port of origin" , "Singles" .)