Crossword Genius

Play ball, throwing a rope, etc, around ring (9)

Ross

I believe the answer is:

cooperate

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

'play ball' is the definition.
(I've seen this before)

'throwing a rope etc around ring' is the wordplay.
I cannot really understand how this works, but
'a' could be 'per' (eg 'one a day' means 'one per day') and 'per' is found within the answer.
'around' could be 'o' (a round letter) and 'o' is found in the answer.
'ring' could be 'o' (letter resembling a ring) and 'o' is present in the answer.
The remaining letters 'cate' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for cooperate that I've seen before include "work hand in glove" , "Work constructively with others" , "getting act together" , "Work together on a common enterprise" , "fit in with others" .)

I've seen this clue in The Times.
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