Sing unto the Lord with the harp - A song or psalm accompanied by the harp. On the harp. See the notes at Isaiah 5:12.
And the voice of a psalm - The voice in singing; a musical voice. Let it not be mere instrumental music, but let that be accompanied with the voice uttering intelligible sounds or words. The only proper use of instrumental music in the worship of God is to deepen the impression which the words are adapted to make; to secure a better influence of truth on the heart.

With - the voice of a Psalm - I think זמרה zimrah, which we translate Psalm, means either a musical instrument, or a species of ode modulated by different voices.

Sing unto the Lord with the harp,.... Playing upon that at the same time: here and in the following verse is an allusion to Old Testament worship, and the manner of performing that; not that this should be done in New Testament times, only New Testament worship is expressed in Old Testament language, which is no unusual thing; hence in Gospel times, and Gospel churches, the saints, especially when singing the new song of redeeming grace, are said to have harps in their hands, expressive only of their spiritual melody in their hearts, Revelation 5:8,
with the harp, and the voice of the psalm; with the harp alone first, as Aben Ezra and Kimchi interpret it, and then with the harp, and together with the words of a psalm, sung in a psalm tune. Gospel churches are to sing psalms, hymns, and spiritual songs, Ephesians 5:19.