Apparently there was some firstfruits of the new covenant even in the time of the Mosaic covenant:
Hebrews 8:10 This is the covenant I will make with the house of Israel after that time, declares the Lord. I will put my laws in their minds and write them on their hearts.
ISA 51:7 Hear me, you who know what is right, you people who have my law in your hearts.
And here is a promise that the Holy Spirit will remain, and not simply come with a temporary empowerment, yet this is in OT times (and see also 1 Chr. 17:13, Hag. 2:5):
Isaiah 59:21 “As for me, this is my covenant with them,” says the Lord. “My Spirit, who is on you, and my words that I have put in your mouth will not depart from your mouth, or from the mouths of your children, or from the mouths of their descendants from this time on and forever,” says the Lord.
“From this time on,” so this started then, and see James 3:3, about how controlling the mouth gives control of the person!