Here's why:
* It describes a noun: We say "a clever person," "a clever solution," etc.
* It can be modified by adverbs: You can say "very clever," "extremely clever," etc.
However, there's a rare instance where "clever" can act as an adverb:
* In informal speech: You might hear someone say, "He answered clever," meaning he answered in a clever way. This usage is not grammatically correct in formal writing, but it's understood in casual conversation.
So, while "clever" is usually an adjective, be aware of that rare adverbial usage in informal situations.