The most recent to lose heart at last? (6)
I believe the answer is:
latest
'last?' is the definition.
('latest' can be a synonym of 'last')
'the most recent to lose heart' is the wordplay.
'the most recent' becomes 'late' (lately means recently).
'to' becomes 'shut' (I've seen this before).
'lose heart' says to hollow out the word (remove centre letters) (I've seen 'lost heart' mean this).
'shut' with its centre taken out is 'st'.
'late'+'st'='LATEST'
'at' is the link.
(Other definitions for latest that I've seen before include "Most recent or most unpunctual" , "Most recent (news)" , "News update" , "hot bit of news" , "most behind time" .)