Wear down hesitation with poem (5)
I believe the answer is:
erode
'wear down' is the definition.
(I've seen this before)
'hesitation with poem' is the wordplay.
'hesitation' becomes 'er'.
'with' says to put letters next to each other.
'poem' becomes 'ode' (ode is a kind of poem).
'er'+'ode'='ERODE'
(Other definitions for erode that I've seen before include "Gradually destroy" , "Eat away" , "Wear away with weather" , "Slowly remove" , "go to pieces!" .)