Pressure sweetheart in careless propositions (8)
I believe the answer is:
premises
'propositions' is the definition.
(I know this)
'pressure sweetheart in careless' is the wordplay.
'pressure' becomes 'p' (abbreviation).
'sweetheart' becomes 'e' (the heart/centre of 'sweet').
'in' is an insertion indicator.
'careless' becomes 'remiss' (I've seen this before).
'e' going inside 'remiss' is 'remises'.
'p'+'remises'='PREMISES'
(Other definitions for premises that I've seen before include "States" , "Property" , "Buildings occupied by businesses" , "Building, place of business" , "propositions that start off arguments" .)