Hard to believe young count (5)
I believe the answer is:
tally
'count' is the definition.
(I know that count can be written as tally)
'hard to believe young' is the wordplay.
'hard to believe' becomes 'tall' (as in a tall tale).
'young' becomes 'y'.
'tall'+'y'='TALLY'
(Other definitions for tally that I've seen before include "Count up; match" , "Record; current score" , "Current score; agree" , "Score; correspond" , "Coincide" .)