Animal has worry about monarch (6)
I believe the answer is:
ferret
'animal' is the definition.
(I've seen this before)
'worry about monarch' is the wordplay.
'worry' becomes 'fret' (fretting is a kind of worrying).
'about' indicates putting letters inside.
'monarch' becomes 'er' (abbreviation for Elizabeth Regina, British Queen).
'fret' going around 'er' is 'FERRET'.
'has' is the link.
(Other definitions for ferret that I've seen before include "Semi-domesticated polecat" , "European polecat bred for hunting rabbits" , "Rabbit-unearthing animal" , "Small fierce animal - good hunting rabbits" , "Root around" .)