alt is an adverb. This phrase contains the adjective alte(r) instead. You must use alter when preceded by the indefinite article ein. When preceded by the definite article der you use alte. This grammar feature is called weak vs strong vs mixed declension of adjectives. Look it up for the full picture.
Minor correction, but "alt" isn't an adverb. It is the noninflected form of the adjective which is used when the adjective is predicative (e.g. er ist alt).