Hesitate to make fathead change (6)
I believe the answer is:
falter
'hesitate' is the definition.
(I know that falter is a more specific form of the action hesitate)
'fathead change' is the wordplay.
'fathead' becomes 'f' (head letter of 'fat').
'change' becomes 'alter' (synonyms).
'f'+'alter'='FALTER'
'to make' acts as a link.
(Other definitions for falter that I've seen before include "Be hesitant" , "Hesitate, waver" , "Hesitate, vacillate" , "Lose momentum" , "Stumble, hesitate" .)