Stopped suppressing annoyance when threatened (10)
I believe the answer is:
endangered
'threatened' is the definition.
('endanger' can be a synonym of 'threaten')
'stopped suppressing annoyance' is the wordplay.
'stopped' becomes 'ended' ('end' can be a synonym of 'stop').
'suppressing' indicates putting letters inside.
'annoyance' becomes 'anger' (I've seen this before).
'ended' placed around 'anger' is 'ENDANGERED'.
'when' acts as a link.
(Other definitions for endangered that I've seen before include "Threatened" , "compromised" , "in a perilous situation" , "put at risk" , "Like some species" .)