Importance of announcement of delay (6)
I believe the answer is:
weight
'importance' is the definition.
(I know that weight is a type of importance)
'announcement of delay' is the wordplay.
'announcement of' indicates a 'sounds like' (homophone) clue.
'delay' becomes 'wait' (synonyms).
'wait' is a homophone of 'WEIGHT'.
'of' acts as a link.
(Other definitions for weight that I've seen before include "Avoir-du-pois" , "Trouble" , "Attach importance to" , "Vertical force exerted by a mass" , "Significance" .)