Hesitate when there's a letter to amend (6)
I believe the answer is:
falter
'hesitate' is the definition.
(I know that falter is a more specific form of the action hesitate)
'a letter to amend' is the wordplay.
'a letter' becomes 'f' ().
'to amend' becomes 'alter' (I've seen this in another clue).
'f'+'alter'='FALTER'
'when there's' is the link.
(Other definitions for falter that I've seen before include "Stumble, hesitate" , "Hesitate, waver" , "flag" , "Lose momentum" , "Hesitate, be uncertain" .)