Keen to get on, engaged by monarch (5)
I believe the answer is:
eager
'keen' is the definition.
(I've seen this before)
'get on engaged by monarch' is the wordplay.
'get on' becomes 'age' (synonyms).
'engaged by' indicates putting letters inside (I've seen this in other clues).
'monarch' becomes 'ER' (abbreviation for Elizabeth Regina).
'age' going into 'er' is 'EAGER'.
'to' acts as a link.
(Other definitions for eager that I've seen before include "Low platform" , "Impatient" , "Enthusiastic, avid" , "Alert and active type?" , "Showing keen interest" .)