The Trinity is the theological construct that God, sometimes referred to as Godhead, is three persons in one: Father, Son, Holy Spirit. Is there evidence of the trinity in the Old Testament, or what Jews call the Tanakh? Yes!
Let’s take a look at Genesis 1:
In the beginning, God created the heavens and the earth. The earth was without form and void, and darkness was over the face of the deep. And the Spirit of God was hovering over the face of the waters.
Verse 2 draws an interesting distinction between God and the Spirit of God. The implication is that the Spirit is still part of God, yet there is enough distinction that the Spirit of God can also be named.
A similar distinction can be seen in Psalm 51:
Create in me a clean heart, O God, and renew a right spirit within me. Cast me not away from your presence, and take not your Holy Spirit from me.
In this passage David speaks to God but also distinguishes or identifies His Holy Spirit as a element or part of God, or what we call today one of the persons of God.