Prime Minister virtually unknown? Shame (4)
I believe the answer is:
pity
'shame' is the definition.
(I know that shame can be written as pity)
'prime minister virtually unknown?' is the wordplay.
'prime minister' becomes 'pitt' (William Pitt the Younger or William Pitt the Elder).
'virtually' means to remove the last letter (virtually all of the word).
'unknown?' becomes 'y' (algebra).
'pitt' with its last letter taken away is 'pit'.
'pit'+'y'='PITY'
(Other definitions for pity that I've seen before include "Feel compassion for" , "unfortunate situation" , "Feel sorrow for" , "Sorrow, compassion" , "Sympathy for the suffering of another" .)