Angry over promise to supply puzzle (9)
I believe the answer is:
crossword
'puzzle' is the definition.
(type of puzzle)
'angry over promise' is the wordplay.
'angry' becomes 'cross' (cross can mean annoyed or angry).
'over' says to put letters next to each other.
'promise' becomes 'word' (as in 'I give you my word').
'cross'+'word'='CROSSWORD'
'to supply' acts as a link.
(Other definitions for crossword that I've seen before include "Letter puzzle" , "Cruciverbal test" , "(Usually) black and white puzzle" , "What's here" , "that should make you think" .)