Skinflint goes crazy munching odd bits of carrot (7)
I believe the answer is:
scrooge
'skinflint' is the definition.
('scrooge' can be a synonym of 'skinflint')
'goes crazy munching odd bits of carrot' is the wordplay.
'crazy' is an anagram indicator.
'munching' is an insertion indicator.
'odd bits of' means one should take alternating letters.
The alternate letters of 'carrot' are 'cro'.
'goes' is an anagram of 'soge'.
'soge' going around 'cro' is 'SCROOGE'.
(Other definitions for scrooge that I've seen before include "One mean with money" , "Mean person" , "Skinflint Ebenezer" , "Miserly curmudgeon" , "Dickens' skinflint (7)" .)