みどり in this sentence is not an adjective, but a noun meaning "greenery".

きれい is an adjective modifying the above noun.

The whole sentence reads then as "It is a town with beautiful greenery".

Either みどりのきれい or みどりがきれい can be used here, see this question.

みどり in this sentence is not an adjective ("green", "greenish"), but a noun meaning "greenery".

きれい is an adjective modifying the above noun.

The whole sentence reads then as "It is a town with beautiful greenery".

が in effect does not connect two adjectives, but a part of relative clause. Either みどりのきれい or みどりがきれい can be used here, see this question.