Fed up, made the mistake of having it postponed (8)
I believe the answer is:
deferred
'postponed' is the definition.
('defer' can be a synonym of 'postpone')
'fed up made the mistake' is the wordplay.
'fed up' becomes 'def' ('fed' going up in a down clue).
'made the mistake' becomes 'erred' (I am not sure about this - if you are sure you should believe this answer much more).
'def'+'erred'='DEFERRED'
'of having it' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for deferred that I've seen before include "Put back" , "Put off to a later time" , "Postponed" .)