Prime Minister pleased with extremely suspect individual (9)
I believe the answer is:
gladstone
'prime minister' is the definition.
(William Ewart Gladstone Prime Minister 1868-1894)
'pleased with extremely suspect individual' is the wordplay.
'pleased' becomes 'glad' (similar in meaning).
'with' means one lot of letters go next to another.
'extremely' says to hollow out the word (remove centre letters) (extreme, outside letters only).
'individual' becomes 'one' (an individual is one person).
'suspect' with its centre taken out is 'st'.
'glad'+'st'+'one'='GLADSTONE'
(Other definitions for gladstone that I've seen before include "C. nineteenth Liberal prime minister" , "So tangled in a small bag like a doctor's" , "Old English P.M. or a doctor's bag" , "Former English PM or kind of bag" , "Tangled so like hinged case" .)