Fur a bit messy on tail of unkempt animal (5,3)
I believe the answer is:
fruit bat
'animal' is the definition.
(fruit bat is a kind of animal)
'fur a bit messy on tail of unkempt' is the wordplay.
'messy' indicates an anagram.
'on' is an insertion indicator (as in clothing 'on' a person).
'tail of' says to take the final letters.
The last letter of 'unkempt' is 't'.
'fur'+'a'+'bit'='furabit'
'furabit' is an anagram of 'fruibat'.
'fruibat' going around 't' is 'FRUIT-BAT'.
(Other definitions for fruit bat that I've seen before include "Long-snouted, large-eyed nectar feeder" , "Flying fox; bait turf (anag.)" , "Flying fox, for example" , "Large flying mammal" .)