Too much fine drinking upset minister, getting sick (8)
I believe the answer is:
overkill
'too much' is the definition.
('overkill' can mean excessive or too much)
'fine drinking upset minister getting sick' is the wordplay.
'fine' becomes 'ok' (synonyms).
'drinking' indicates putting letters inside.
'upset minister getting' becomes 'ver' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'sick' becomes 'ill' (similar in meaning).
'ok' placed around 'ver' is 'overk'.
'overk'+'ill'='OVERKILL'
Can you help me to learn more?
(Other definitions for overkill that I've seen before include "Excessive action, armament" , "much more than required" , "Hyperbole" , "Excessive amount" , "Ridiculous excess" .)