Worry about Her Majesty's search (6)
I believe the answer is:
ferret
'search' is the definition.
(ferreting is a kind of searching)
'worry about her majesty's' is the wordplay.
'worry' becomes 'fret' (fretting is a kind of worrying).
'about' is an insertion indicator.
'her majesty' becomes 'er' (Elizabeth Regina).
'fret' enclosing 'er' is 'FERRET'.
(Other definitions for ferret that I've seen before include "Semi-domesticated polecat" , "Small polecat" , "Small fierce animal - good hunting rabbits" , "Rabbit-hunting polecat" , "Rabbit-unearthing animal" .)