Endless sin, in that degree, will engage Rector and other ministers (6)
I believe the answer is:
vicars
'ministers' is the definition.
(I've seen this before)
'endless sin in that' is the wordplay.
'endless' means to remove the last letter.
'sin' becomes 'vice'.
'in that' becomes 'ars' (I can't justify this - if you can you should give a lot more credence to this answer).
'vice' with its last letter removed is 'vic'.
'vic'+'ars'='VICARS'
'degree will engage rector and other' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for vicars that I've seen before include "clergymen" , "Ministers" , "those taking tarts to party" , "Members of clergy in charge of churches" .)