Scrutinise monarch, for example, holding power (7)
I believe the answer is:
inspect
'scrutinise' is the definition.
(I've seen this before)
'monarch for example holding power' is the wordplay.
'monarch for example' becomes 'insect' (monarch is a kind of insect).
'holding' is an insertion indicator.
'power' becomes 'p'.
'insect' placed around 'p' is 'INSPECT'.
(Other definitions for inspect that I've seen before include "Look critically at" , "Check" , "Scan" , "Go over" , "vet" .)