Does this sentence Kate was always helpful contain a passive verb?

This sentence is an active sentence because we can see who the subject is = Kate.

was = verb
always = adverb
helpful = adjective

Passive verbs have the form -- be verb + past participle.

We were helped

by Kate. = passive sentence.

By + noun tells us who or what does the action in a passive sentence. But it is not necessary to say who the actor is. eg

The Mona Lisa was painted

in the 16th century.(by Leonardo da vinci)