Old dog deserves short starting price (4)
I believe the answer is:
odds
'price' is the definition.
(I've seen this before)
'old dog deserves short starting' is the wordplay.
'starting' says to take the initial letters.
The initial letters of 'old dog deserves short' is 'ODDS'.
(Other definitions for odds that I've seen before include "(In betting) chances" , "The likelihood of something occurring rather than not" , "The chances of something happening" , "at which one may be disagreeing" , "Chance" .)