Protest, at which action directed (6)
I believe the answer is:
I believe this clue is a double definition.
'protest' is the first definition.
(as in objecting to something)
'at which action directed' is the second definition.
(object can mean a purpose or target)
(Other definitions for object that I've seen before include "offer in opposition", "Argue against - purpose", "Protest, disapprove", "part of sentence", "Express dissent to the thing?".)