After a professor, one's becoming fellow (6)
I believe the answer is:
adonis
'fellow' is the definition.
(I have seen 'Handsome fellow' mean 'adonis' so perhaps 'fellow' could also mean 'adonis')
'after a professor one's' is the wordplay.
'after' says to put letters next to each other.
'professor' becomes 'don' (I've seen this before).
'one's' becomes 'I's' (Roman numeral).
'a' put next to 'don' is 'adon'.
'adon'+'is'='ADONIS'
'becoming' is the link.
(Other definitions for adonis that I've seen before include "one deemed to be beautiful" , "Handsome youth (Gr.)" , "Aphrodite's love" , "dish" , "Hunk" .)