Influential part abandoned by fine thespian (5)
I believe the answer is:
actor
'thespian' is the definition.
(synonyms)
'influential part abandoned by fine' is the wordplay.
I cannot really understand how this works, but
'part' could be 'act' (I have seen 'Part of play ' mean 'act' so perhaps 'part' could also mean 'act') and 'act' is found in the answer.
The remaining letters 'or' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for actor that I've seen before include "One taking part" , "Player - performer" , "Theatrical performer" , "one to take on roles" , "Luvvy" .)