Support the postponement (4)
I believe the answer is:
stay
I believe this clue is a double definition.
'support' is the first definition.
(stay is a kind of support)
'the postponement' is the second definition.
(thesaurus)
(Other definitions for stay that I've seen before include "lodge" , "Remain; steady" , "guy to > put off" , "Temporary residence" , "Stick around" .)