Object, with annoyance, to risk (8)
I believe the answer is:
endanger
'to risk' is the definition.
(to risk is to put in danger)
'object with annoyance' is the wordplay.
'object' becomes 'end' (I've seen this in other clues).
'with' says to put letters next to each other.
'annoyance' becomes 'anger' (I've seen this before).
'end'+'anger'='ENDANGER'
(Other definitions for endanger that I've seen before include "Imperil" , "Put in peril" , "Put in harm's way" , "Pose a threat to" , "Put in jeopardy" .)