Little cared for being petty (5-6)
I believe the answer is:
small-minded
'being petty' is the definition.
(I've seen this before)
'little cared' is the wordplay.
'little' becomes 'small' (synonyms).
'cared' becomes 'minded' (I've seen this before).
'small'+'minded'='SMALL-MINDED'
'for' is the link.
(Other definitions for small-minded that I've seen before include "Petty" , "Intolerant" .)