Tree-dweller shot off holding end of tail (5)
I believe the answer is:
sloth
'tree-dweller' is the definition.
'shot off holding end of tail' is the wordplay.
'off' indicates an anagram.
'holding' is an insertion indicator.
'end of' indicates one should take the final letters.
The last letter of 'tail' is 'l'.
'shot' is an anagram of 'soth'.
'soth' placed around 'l' is 'SLOTH'.
(Other definitions for sloth that I've seen before include "Arboreal animal" , "Deadly offence" , "One's often suspended from tree" , "A deadly sin, being lazy" , "Sluggish creature" .)