Happening briefly in flat (4)
I believe the answer is:
even
'flat' is the definition.
('even' can be similar in meaning to 'flat')
'happening briefly' is the wordplay.
'happening' becomes 'event' (I've seen this before).
'briefly' means to remove the last letter.
'event' with its last letter taken away is 'EVEN'.
'in' is the link.
(Other definitions for even that I've seen before include "end of the day, reading poetry" , "time of day" , "Short joke" , "without a rise?" , "Level, calm" .)