Public official is gracious I aver, finally (7)
I believe the answer is:
coroner
'public official' is the definition.
(I've seen this before)
'gracious i aver finally' is the wordplay.
'gracious' becomes 'cor' (both are exclamations of surprise).
'i' becomes 'one' (Roman numeral for one).
'finally' suggests the final letters.
The final letter of 'aver' is 'r'.
'cor'+'one'+'r'='CORONER'
'is' is the link.
(Other definitions for coroner that I've seen before include "President of inquests" , "Legal figure" , "Official who investigates sudden deaths" , "Investigator" , "One presides at inquests" .)