Flipping annoyed on backing corrupt fighters in ring (7)
I believe the answer is:
toreros
'fighters in ring' is the definition.
(fighters in a bullring)
'flipping annoyed on backing corrupt' is the wordplay.
'flipping' is a reversal indicator.
'annoyed' becomes 'sore' (I've seen this in another clue).
'on' means one lot of letters go next to another.
'backing' says the letters should be written backwards.
'corrupt' becomes 'rot'.
'sore' backwards is 'eros'.
'rot' reversed gives 'tor'.
'eros' put after 'tor' is 'TOREROS'.
(Another definition for toreros that I've seen is " Bullfighters".)