Fellow competitor running ablest team (10)

I believe the answer is:

stablemate

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'fellow' is the definition.
(stablemate can mean a fellow or colleague)

'running ablest team' is the wordplay.
'running' indicates anagramming the letters (the letters run around to different places).
'ablest'+'team'='ablestteam'
'ablestteam' is an anagram of 'STABLEMATE'.

'competitor' is the link.
I am not very happy about this link. It may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for stablemate that I've seen before include "person in same outfit" , "Maybe fellow Arab" , "colleague in same organization" , "Blames Tate (anag) - person from the same club" , "One from the same organisation as another" .)

I've seen this clue in The Times.

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