Before leaving Sinai, Moses invited his father-in-law to stay with the Israelites and accompany them to the promised land. He must have accepted, or perhaps he came back 40 years later, since the Kenites are later recorded as having settled in the Desert of Judah, possibly somewhere near Jericho (also called the City of Palms).
Jethro is given different names in different places: Jethro/Jether (Ex. 4:18), Hobab (Num. 10:29; Jud. 4:11) and Reuel (Ex. 2:18). The name Reuel could also be a family (or clan) names. This variation has been attributed to there being different writers of the various texts, changes in usage over time (like we might call someone John Smith, Johnathan, Jonno, Jon, Smithy, or even JS), or that each name shows a different part of Jethro’s relationship to God and the scriptures. Take your pick.
Some of his activities are discussed in this article about Jethro/Hobab’s detainment.