Nun's supervisor's earlier attempts half-forgotten (8)
I believe the answer is:
prioress
'nun's' is the definition.
(I have seen 'Superior nun ' mean 'prioress' so perhaps 'nun' could also mean 'prioress')
'earlier attempts half-forgotten' is the wordplay.
'earlier' becomes 'prior' (synonyms).
'attempts' becomes 'essays' (I've seen this before).
'half forgotten' indicates taking half.
'essays' cut in half is 'ess'.
'prior'+'ess'='PRIORESS'
'supervisor's' acts as a link.
This may not be right. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for prioress that I've seen before include "Superior nun" , "A senior member of a female religious house" , "Religious leader" .)