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Coach further, and keep, outside right (7)

Ross

I believe the answer is:

retrain

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'coach further and' is the definition.
I can't judge whether this defines the answer.

'keep outside right' is the wordplay.
'keep' becomes 'retain' (synonyms).
'outside' means one lot of letters goes inside another (some letters go outside others).
'right' becomes 'r' (common abbreviation).
'retain' enclosing 'r' is 'RETRAIN'.

Can you help me to learn more?

(Other definitions for retrain that I've seen before include "Teach (someone) new skills" , "Learn new skills" , "Prepare for new job" , "coach yet again" , "ready for a new assignment" .)

I've seen this clue in The Times.
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