The scriptures do not reference a music ministry. Yes, David may have paid musicians to play in the temple, but that does not constitute a ministry, but rather a job or an office. An office is not the same thing as a ministry, else there would be a ministry of secretary and usher and…you get the idea.

Ephesians 4:11-13
4:11 And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers;
4:12 For the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ:
4:13 Till we all come in the unity of the faith, and of the knowledge of the Son of God, unto a perfect man, unto the measure of the stature of the fulness of Christ: