Former president is human being without the first bit of sense (5)
I believe the answer is:
peron
'former president' is the definition.
(Juan Peron, Argentine president)
'human being without the first bit of sense' is the wordplay.
'human being' becomes 'person' (I've seen this before).
'without' is a deletion indicator.
'the first bit of sense' becomes 's' (1st letter of 'sense').
'person' with 's' taken out is 'PERON'.
'is' acts as a link.
(Other definitions for peron that I've seen before include "Former Argentine leader" , "Argentinian president, Evita his wife" , "Juan ---, Argentine dictator" , "Argentinian dictator, 1946-55" , "Juan, maybe" .)