Fight roughly, the first to be thrown out (4)
I believe the answer is:
bout
'fight' is the definition.
(synonyms)
'roughly the first to be thrown out' is the wordplay.
'roughly' becomes 'about' (synonyms).
'the first' becomes 'a'.
'to be thrown out' is a deletion indicator.
'about' with 'a' taken away is 'BOUT'.
(Other definitions for bout that I've seen before include "Period of illness or boxing match" , "Wrestling contest" , "Period of activity or boxing contest" , "Spell of eg drinking" , "Attack (of illness)" .)