The first prayer is the people crying out to God in the end of ch 2
God then appears “in person” in the burning bush, and talk to Moses. After that, there are a number of instances of God and Moses speaking directly.
The next reference to “prayer” comes when Pharaoh asks Moses to pray for him to the Lord to remove a plague (8:8-9. 28-29, 9:28, 10:17). Again, as in Genesis, this use of the word “pray” seems to mean “intercede” rather than just “talk to God”.