Start to despair (4,5)
I believe the answer is:
lose heart
'start to despair' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for lose heart that I've seen before include "Become despondent" , "Start to despair" , "Let hopes dwindle - real ethos involved" , "find discouragement" , "Become dispirited" .)