Is his a possessive pronoun

Yes, the Word 'his' is a possessive pronoun and a possessive adjective.

A possessive pronoun is a Word that takes the place of a noun that belongs to someone or something.

Example: Jack lives on this street. The house on the corner is his.

A possessive adjective is a Word that is placed before a noun to describe that noun as belonging to someone or something.

Example: Jack lives on this street. Hishouse is on the corner.