Hello!
An adjective is something that describes a noun. For example, if you said "The dog is cute," the word cute would be the adjective because it describes the noun (dog).
"Climbs the stairs" is not considered an adjective. This is because nothing describes the stairs or how the person may have climbed them. The phrase would be considered a verb phrase because "to climb the stairs" is an action.
I hope this helps you! Have a great day!