Fellow irritates nameless supervisors (8)
I believe the answer is:
managers
'supervisors' is the definition.
(a manager supervises employees)
'fellow irritates nameless' is the wordplay.
I cannot quite understand how this works, but
'fellow' could be 'man' (fellow can mean a man) and 'man' is present in the answer.
This may be the basis of clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for managers that I've seen before include "Executives, administrators" , "Executives, overseers" , "Sports team chiefs" , "Coping" .)