I had upset minister who runs a business? (8)
I believe the answer is:
director
'business?' is the definition.
(I know that director is a profession)
'i had upset minister' is the wordplay.
'i had' becomes 'I'd' (contraction).
'upset' says the letters should be written backwards.
'minister' becomes 'rector' (synonyms).
'id' back-to-front is 'di'.
'di'+'rector'='DIRECTOR'
'who runs a' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for director that I've seen before include "Company board member" , "leader" , "Big cheese" , "Boss posing as creditor" , "Senior person in a firm, executive or non-executive" .)