Wear down hesitation before poem (5)
I believe the answer is:
erode
'wear down' is the definition.
(to erode is to wear down or decay)
'hesitation before poem' is the wordplay.
'hesitation' becomes 'er' (sound made while hesitating - um, er).
'before' means one lot of letters go next to another.
'poem' becomes 'ode' (ode is a type of poem).
'er'+'ode'='ERODE'
(Other definitions for erode that I've seen before include "Slowly remove" , "fragment" , "Abrade" , "Gradually destroy" , "go to pieces!" .)