The fur after some hesitation belongs to me (6)
I believe the answer is:
ermine
'the fur' is the definition.
(ermine is a kind of fur)
'some hesitation belongs to me' is the wordplay.
'some hesitation' becomes 'erm'.
'belongs' becomes 'ne' (I can't justify this - if you can you should give a lot more credence to this answer).
'to' is a charade indicator (letters next to each other) (I've seen this in other clues).
'me' becomes 'I'.
'ne' after 'i' is 'ine'.
'erm'+'ine'='ERMINE'
'after' acts as a link.
Can you help me to learn more?
(Other definitions for ermine that I've seen before include "Fur-bearing mammal" , "Animal with brown fur that turns white in winter" , "Expensive white fur" , "White fur from kind of 25 Across - judges may wear it" , "White-coated stoat" .)