How is that the Holy Spirit is in the Old Testament?

God, Helper, Jesus

I am surprised every time when I see the Holy Spirit in the Old Testament. Psa 51:11 Cast me not away from your presence, and take not your Holy Spirit from me. Does that mean God has a Holy Spirit before Jesus was born? Some of these questions I do not know the answer to. But I will explore more. Isa 63:10 But they rebelled and grieved his Holy Spirit;
therefore he turned to be their enemy, and himself fought against them. Reading the whole verse I find the Headline

Create in Me a Clean Heart, O God

That is amazing. Sometimes I find reading the Old Testament tough. But it may be something as equally important to dive into as the New Testament. I felt God tell me this morning to skip the 7:00 news and continue in my word. I discovered something new.  Thanks for reading.