Keen on hosting monarch for a start (5)
I believe the answer is:
intro
'a start' is the definition.
(I've seen this before)
'keen on hosting monarch' is the wordplay.
'keen on' becomes 'into' (I've seen this before).
'hosting' is an insertion indicator.
'monarch' becomes 'r' (r is abbreviation for rex).
'into' enclosing 'r' is 'INTRO'.
'for' is the link.
(Other definitions for intro that I've seen before include "starter" , "Opener" , "overture" , "Preamble" , "First part of a news story (abbr)" .)