Feels upset about a race finish that cheats! (7)

I believe the answer is:

fleeces

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

'cheats' is the definition.
(I know this)

'feels upset about a race finish' is the wordplay.
'upset' indicates an anagram.
'about' indicates putting letters inside.
'a race finish' becomes 'ce' (I am not sure about this - if you are sure you should believe this answer much more).
'feels' anagrammed gives 'flees'.
'flees' placed around 'ce' is 'FLEECES'.

'that' is the link.

Can you help me to learn more?

(Other definitions for fleeces that I've seen before include "Rips off" , "Ovine coats" , "layer[S?] of clothing" .)

I've seen this clue in the Evening Standard.

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