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Throwing couple of rights, initially fear punch-up (9)

Ross

I believe the answer is:

fistfight

I'm a little stuck... Click here to teach me more about this clue!

'punch-up' is the definition.
(both can mean a fight)

'throwing couple of rights initially fear' is the wordplay.
I cannot really see how this works, but
'initially' could be 'ist' (ist resembles 1st) and 'ist' is found in the answer.
This may be the basis of the clue (or it may be nonsense).

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