Disinclined to declare since losing heart (6)
I believe the answer is:
averse
'disinclined to' is the definition.
(I've seen this before)
'declare since losing heart' is the wordplay.
'declare' becomes 'aver' (averring is a kind of declaring).
'losing heart' suggests removing the centre.
'since' with its centre removed is 'se'.
'aver'+'se'='AVERSE'
(Other definitions for averse that I've seen before include "Disinclined - as ever (anag)" , "A line of poetry is opposed" , "Having a strong dislike" , "Disinclined, maybe to hard work" , "Unwilling or disinclined, perhaps to hard work" .)