Starr reportedly had taste for this meat back in short supply (7)
I believe the answer is:
hamster
'starr reportedly had taste for this' is the definition.
The definition suggests a singular noun which matches the answer.
'meat back in short supply' is the wordplay.
'meat' becomes 'ham' (ham is a kind of meat).
'back' becomes 'stern' (I've seen this before).
'in short supply' means to remove the last letter.
'stern' with its last letter taken away is 'ster'.
'ham'+'ster'='HAMSTER'
Can you help me to learn more?
(Other definitions for hamster that I've seen before include "Little beast" , "Rodent often kept as pet" , "one running round in circles?" , "Animal" , "Short-tailed burrowing rodent" .)