Hesitated to have the figurehead changed (8)
I believe the answer is:
faltered
'hesitated' is the definition.
(faltering is a kind of hesitating)
'the figurehead changed' is the wordplay.
'the figurehead' becomes 'f' (head letter of 'figure').
'changed' becomes 'altered' ('alter' can be a synonym of 'change').
'f'+'altered'='FALTERED'
'to have' acts as a link.
(Other definitions for faltered that I've seen before include "was hesitant" , "Failed" , "Hesitated, moved unsteadily" .)