Test introduced by prime minister related to public office (7)
I believe the answer is:
mayoral
'related to public office' is the definition.
I can't tell whether this defines the answer.
'test introduced by prime minister' is the wordplay.
'test' becomes 'oral' (oral is a type of examination).
'introduced by' means one lot of letters go next to another.
'prime minister' becomes 'may' (I've seen this in other clues).
'oral' put after 'may' is 'MAYORAL'.
Can you help me to learn more?
(Other definitions for mayoral that I've seen before include "town office" , "for chief councillor?" , "council leader" , "Relating to city leader" , "Of a civic dignitary" .)