People start to demand fix (4)
I believe the answer is:
mend
'fix' is the definition.
('mend' can be a synonym of 'fix')
'people start to demand' is the wordplay.
'people' becomes 'men' (man is a kind of person).
'start to' suggests taking the first letters.
The first letter of 'demand' is 'd'.
'men'+'d'='MEND'
(Other definitions for mend that I've seen before include "'Restore, fix (4)'" , "Make improvements" , "Return to health; repair" , "Fix, repair" , "Put right" .)