Chief part of the monarchy (4)
I believe the answer is:
arch
'chief' is the definition.
(synonyms)
'part of the monarchy' is the wordplay.
'part of' indicates a hidden word.
'ARCH' is hidden within 'monarchy'.
(Other definitions for arch that I've seen before include "a piece about a foot?" , "Marble, for example" , "Bridge span" , "Structural curve" , "Roguish - superior" .)