Embarrassed by horse going astray — it's a distraction (3,7)
I believe the answer is:
red herring
'a distraction' is the definition.
(distracting false clue)
'embarrassed by horse going astray' is the wordplay.
'embarrassed' becomes 'red' (someone may blush or go red when embarrassed).
'by' says to put letters next to each other.
'horse' becomes 'H' (abbreviation as in horse power).
'going astray' becomes 'erring' (err can mean to go the wrong way).
'red'+'h'+'erring'='RED HERRING'
'it's' is the link.
(Other definitions for red herring that I've seen before include "Distraction" , "False lead" , "(Fishy) diversion" , "It may well put you off" , "An irrelevance" .)