Is clever a word or is the term more clever?

"Clever" is a word, and "more clever" is the comparative form of that word.

* Clever is an adjective that describes someone or something as intelligent, skillful, or quick-witted.

* More clever is used when comparing two or more things or people in terms of their cleverness, indicating that one is more intelligent, skillful, or quick-witted than the other(s).

So, both "clever" and "more clever" are correct terms, but they are used in different contexts.