Is tense a part of speech?

Yes, the Word tense has a part of speech. In English, all Words can function as at least one part of speech. Tense can be used as an adjective, a verb, and a noun.

Adjective: The physical therapist can massage tense muscles.

Verb: Haley's muscles tensed up.

Noun: A verb tense shows when an action happened or will happen.