Mastery involves one's endless commitment to the cloister (9)
I believe the answer is:
monastery
'to the cloister' is the definition.
(monastery is a kind of cloister)
'mastery involves one's endless' is the wordplay.
'involves' indicates putting letters inside.
'endless' means to remove the last letter.
'one' with its final letter taken off is 'on'.
'mastery' placed around 'on' is 'MONASTERY'.
'commitment' acts as a 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 monastery that I've seen before include "One vows to stay here" , "Religious establishment" , "Where brothers gather" , "Residence of religious community" , "Religious house" .)