Somehow let a horse become discouraged (4,5)
I believe the answer is:
lose heart
'become discouraged' is the definition.
(I've seen this before)
'somehow let a horse' is the wordplay.
'somehow' is an anagram indicator.
'let'+'a'+'horse'='letahorse'
'letahorse' anagrammed gives 'LOSE HEART'.
(Other definitions for lose heart that I've seen before include "Start to despair" , "find discouragement" , "Here's a lot to cause courage to ebb" , "Become dispirited" , "Falter in courage - or fall in love? (4, 5)" .)