Is then an adjective or an adverb?

Answer 1

The word "then" is usually an adverb of time or sequence (after, following, next).

It can be considered an adjective when it is attached to a noun (the then-leader of the cult) as opposed to an adjective (the then-common practice). It may be considered a noun when used with a preposition (until then).

Answer 2

The word then is usually an adverb, and arguably a noun as well. It may also be an adjective when used to modify a noun e.g. "the then-director of the CIA."