PET is used before these nouns:
scan

domestic, family, house, household
beloved
the loss of a beloved pet

abandoned, unwanted
lost
if you need help locating your lost pet

exotic
the booming trade in exotic pets

virtual
the latest wave of toy technology: virtual pets

have, keep, own
allow
The apartment we live in doesn't allow pets of any kind.

feed
Feed your pet a healthy diet.

shop (esp. BrE), store (esp. AmE)
cat, dog, rabbit, etc.
owner
sitter
Some pet sitters charge on a per-visit basis.

care
the pet care industry

trade
the smuggling of endangered species for the pet trade

food
dander (esp. AmE), hair
people who are allergic to pet dander
a vacuum cleaner that can tackle pet hair

allergy
kids with pet allergies

carrier
She bundled Daisy into her pet carrier.

Pet is used with these nouns as the object:
cat, dog

Pet is used with these nouns:
cause, hate, name, project, subject, theory