Is "is" a verb? If not, what is the verb in this sentence: "Although the school is quite small, it has a lovely field for students to play in."?

Yes.

Is is a linking verb.

Is is a linking verb. It links or connects the subject "school" to the predicate adjective "small".

Note: "Although the school is quite small" is a dependent clause.

Another verb in the sentence is found in the independent clause "it has a lovely field for students to play in".

The other verb is has .