* ὑψόω (hupsoō): This means "to lift up," "to raise," or "to elevate," and is often used in a literal or figurative sense, including the exaltation of someone's status or power. This is probably the closest single word.
* ἐπαινέω (epaineō): This means "to praise," "to commend," or "to applaud." While not directly "exalt," it often implies the raising of someone's reputation or esteem.
* δοξάζω (doxazō): This means "to glorify," "to honor," or "to give glory to." This is suitable if the exaltation involves giving glory or honor to a deity or a person.
The best choice will depend on the context. For a general sense of raising someone's status or importance, ὑψόω (hupsoō) is likely the most appropriate.