I must go in to protest at decline (10)
I believe the answer is:
depreciate
'decline' is the definition.
(thesaurus)
'i must go in to protest' is the wordplay.
'must go in to' is an insertion indicator.
'protest' becomes 'deprecate' (deprecate can mean to object to or protest against).
'i' put within 'deprecate' is 'DEPRECIATE'.
'at' is the link.
(Other definitions for depreciate that I've seen before include "Lose value with time" , "Gradually lose value" , "Belittle; lose value" .)