Man probing English prime minister's nickname (7)
I believe the answer is:
epithet
'nickname' is the definition.
(I've seen this before)
'man probing english prime minister's' is the wordplay.
'man' becomes 'he' (he refers to a man).
'probing' means one lot of letters goes inside another (probe can mean to make a hole in).
'english' becomes 'E' (abbreviation).
'prime minister' becomes 'Pitt' (William Pitt the Younger or William Pitt the Elder).
'e'+'pitt'='epitt'
'he' placed within 'epitt' is 'EPITHET'.
(Other definitions for epithet that I've seen before include "Adjective expressing some quality of a person" , "title" , "nickname" , "What characterises" , "Descriptive adjective" .)