Ran away riding a horse that's tired (7)

I believe the answer is:

flagged

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

'ran away riding a horse' is the wordplay.
'ran away' becomes 'fled' (I've seen this before).
'riding' indicates putting letters inside (some letters sit around or 'ride' others).
'horse' becomes 'gg'.
'a'+'gg'='agg'
'fled' enclosing 'agg' is 'FLAGGED'.

'that's' acts as a link.

(Another definition for flagged that I've seen is " tired".)

I've seen this clue in The Guardian.

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