Monk gets king into trouble (7)
I believe the answer is:
brother
'monk' is the definition.
(title for a monk)
'king into trouble' is the wordplay.
'king' becomes 'R' (abbreviation for rex, king in Latin).
'into' means one lot of letters goes inside another.
'trouble' becomes 'bother' (synonyms).
'r' put into 'bother' is 'BROTHER'.
'gets' is the link.
(Other definitions for brother that I've seen before include "Union member - male relative" , "Relation" , "Close relative" , "Trade unionist" , "Male sibling" .)