Anxiety about pet in case of bullets (9)
I believe the answer is:
cartouche
'case of bullets' is the definition.
(I've seen this before)
'anxiety about pet' is the wordplay.
'anxiety' becomes 'care' (care is a kind of anxiety).
'about' is an insertion indicator.
'pet' becomes 'touch' (to pet an animal is to touch it affectionately).
'care' placed around 'touch' is 'CARTOUCHE'.
'in' acts as a link.
(Other definitions for cartouche that I've seen before include "Ornate frame around an inscription" , "decorative ornament" , "Carved decoration in the shape of a scroll" , "case of bullets" , "Carved tablet for inscription" .)