is this a run-on sentence? Niabi play both the oboe and the piano and plays them well.

No, it's not a run-on, but there is a subject-verb agreement problem here.

Subject - Niabi (s.)
Verbs - play (pl.) ... plays (s.)

How will you correct this?

http://grammar.ccc.commnet.edu/grammar/sv_agr.htm

Yes, the sentence "Niabi play both the oboe and the piano and plays them well." is a run-on sentence. In order to identify run-on sentences, it is helpful to understand the structure of a sentence.

A complete sentence should have a subject (who or what the sentence is about) and a predicate (what the subject is doing or what is being said about the subject). A run-on sentence occurs when two or more independent clauses (complete thoughts) are joined together without proper punctuation.

To fix this run-on sentence, you can use several methods. One way is to separate the two independent clauses into two separate sentences:

"Niabi plays the oboe well. She also plays the piano well."

Alternatively, you can separate the two clauses by using a coordinating conjunction such as "and" or "but":

"Niabi plays both the oboe and the piano, and she plays them well."

Remember, a run-on sentence can also be fixed by using a semicolon (;) to separate the independent clauses:

"Niabi plays both the oboe and the piano; she plays them well."

By using these techniques, you can create clear and grammatically correct sentences.