Put at risk, cease to be annoyed? (8)
I believe the answer is:
endanger
'put at risk' is the definition.
(I've seen this before)
'cease to be annoyed?' is the wordplay.
'cease' becomes 'end' (synonyms).
'to be annoyed?' becomes 'anger' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'end'+'anger'='ENDANGER'
Can you help me to learn more?
(Other definitions for endanger that I've seen before include "Hazard" , "Jeopardize" , "Dan Green (anag.)" , "Pose a threat to" , "To put one at risk" .)