Keen to make impression, supporting a monarch (6)
I believe the answer is:
ardent
'keen' is the definition.
(I've seen this before)
'impression supporting a monarch' is the wordplay.
'impression' becomes 'dent' (dent is a kind of impression**).
'supporting' means one lot of letters go next to another (in a down clue, some letters go below others).
'monarch' becomes 'r' (r is abbreviation for rex).
'a'+'r'='ar'
'dent' put after 'ar' is 'ARDENT'.
'to make' acts as a link.
(Other definitions for ardent that I've seen before include "Loving and fiery" , "Intensely devoted" , "Ranted badly and became earnest in love" , "Intensely enthusiastic" , "Ranted, being passionate" .)