Is trust a verb

Trust as in to believe in the reliably of something or a person (such as this answer) is an action and therefore a verb.

Trust as in an organisation (ie - hospital trust) is a place and therefore a noun.

A verb is a Word that describes an action (run, walk, etc), a state of being (exist, stand, etc) or occurrence (happen, become, etc).

A noun is a Word that is used to describe a person (man, lady, teacher, etc), place (home, city, beach, etc) or thing (car, banana, book, etc).