The old dear loses head, getting a horse (8)
I believe the answer is:
yearling
'a horse' is the definition.
(yearling is a kind of horse)
'the old dear loses head getting' is the wordplay.
'the old' becomes 'ye'.
'dear' becomes 'darling' ('darling' can be a synonym of 'dear').
'loses head' means to remove the first letter.
'getting' is a charade indicator (letters next to each other).
'darling' with its first letter taken off is 'arling'.
'ye'+'arling'='YEARLING'
(Other definitions for yearling that I've seen before include "Animal in its second year" , "Relaying (anag.)" , "Youngster" , "Sort of racehorse" , "Twelve-month old animal" .)