Anthem: keen on it when rector enters (7)
I believe the answer is:
introit
'anthem' is the definition.
(I've seen this before)
'on it when rector enters' is the wordplay.
'on' means one lot of letters go next to another.
'when' becomes 'into' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'rector' becomes 'r'.
'enters' is an insertion indicator.
'into' enclosing 'r' is 'intro'.
'it' put after 'intro' is 'INTROIT'.
'keen' is the link.
This may not be right. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for introit that I've seen before include "piece of church music" , "Short prayer" , "chant" , "Anthem sung at beginning of Mass" , "Pre-Eucharist prayer" .)