Tree, thinner on top having been pollarded (5)
I believe the answer is:
alder
'tree' is the definition.
(alder is a kind of tree)
'thinner on top having been pollarded' is the wordplay.
'thinner on top' becomes 'balder'.
'having been pollarded' means to remove the first letter (to pollard a tree is to cut off tops of branches).
'balder' with its first letter removed is 'ALDER'.
(Other definitions for alder that I've seen before include "Artificial fishing fly" , "North temperate tree with cone-like fruit" , "Tree growing in damp ground" , "Birch relative" , "Tree whose bark is used in tanning" .)