Geshur was a region to the east of the Sea of Galilee within Aram where Golan Heights and Syria now are found.
After Moses died, Joshua led the Israelite campaigns to take the lands promised to Abraham's descendants -
Joshua 12:1-5:
1. These are the kings of the land whom the Israelites had defeated and whose territory they took over east of the Jordan, from the Arnon Gorge to Mount Hermon, including all the eastern side of the Arabah:
2. Sihon king of the Amorites, who reigned in Heshbon. He ruled from Aroer on the rim of the Arnon Gorge--from the middle of the gorge--to the Jabbok River, which is the border of the Ammonites. This included half of Gilead.
3. He also ruled over the eastern Arabah from the Sea of Kinnereth to the Sea of the Arabah (the Salt Sea), to Beth Jeshimoth, and then southward below the slopes of Pisgah.
4. And the territory of Og king of Bashan, one of the last of the Rephaites, who reigned in Ashtaroth and Edrei.
5. He ruled over Mount Hermon, Salecah, all of Bashan to the border of the people of Geshur and Maacah, and half of Gilead to the border of Sihon king of Heshbon.
Joshua 13:1-13 described the partitioning of Canaan in the former region of Bashan:
1. When Joshua was old and well advanced in years, the LORD said to him, "You are very old, and there are still very large areas of land to be taken over.
2. "This is the land that remains: all the regions of the Philistines and Geshurites:
3. from the Shihor River on the east of Egypt to the territory of Ekron on the north, all of it counted as Canaanite (the territory of the five Philistine rulers in Gaza, Ashdod, Ashkelon, Gath and Ekron--that of the Avvites);
4. from the south, all the land of the Canaanites, from Arah of the Sidonians as far as Aphek, the region of the Amorites,
5. the area of the Gebalites; and all Lebanon to the east, from Baal Gad below Mount Hermon to Lebo Hamath.
6. "As for all the inhabitants of the mountain regions from Lebanon to Misrephoth Maim, that is, all the Sidonians, I myself will drive them out before the Israelites. Be sure to allocate this land to Israel for an inheritance, as I have instructed you,
7. and divide it as an inheritance among the nine tribes and half of the tribe of Manasseh."
8. The other half of Manasseh, the Reubenites and the Gadites had received the inheritance that Moses had given them east of the Jordan, as he, the servant of the LORD, had assigned it to them.
9. It extended from Aroer on the rim of the Arnon Gorge, and from the town in the middle of the gorge, and included the whole plateau of Medeba as far as Dibon,
10. and all the towns of Sihon king of the Amorites, who ruled in Heshbon, out to the border of the Ammonites.
11. It also included Gilead, the territory of the people of Geshur and Maacah, all of Mount Hermon and all Bashan as far as Salecah--
12. that is, the whole kingdom of Og in Bashan, who had reigned in Ashtaroth and Edrei and had survived as one of the last of the Rephaites. Moses had defeated them and taken over their land.
13. But the Israelites did not drive out the people of Geshur and Maacah, so they continue to live among the Israelites to this day.
Considering other passages about Havvoth Jair, Arameans and Isarelites fought over towns in the region until the time of David. According to this passage, some of the towns taken by Segub had been taken back by Arameans,
1 Chronicles 3:22-23:
22. Segub was the father of Jair, who controlled twenty-three towns in Gilead.
23. (But Geshur and Aram captured Havvoth Jair, as well as Kenath with its surrounding settlements--sixty towns.) All these were descendants of Makir the father of Gilead.
2 Samuel 3:3 identified a king named Talmai during the reign of David. David took Talmai's daughter, Maacah as a wife who bore him Absalom.
Verse 2 of 1 Chronicles 3:1-3 also spoke of Absalom:
1. These were the sons of David born to him in Hebron: The firstborn was Amnon the son of Ahinoam of Jezreel; the second, Daniel the son of Abigail of Carmel;
2. the third, Absalom the son of Maacah daughter of Talmai king of Geshur; the fourth, Adonijah the son of Haggith;
3. the fifth, Shephatiah the son of Abital; and the sixth, Ithream, by his wife Eglah.
Absalom was raised with other offspring of David's including Amnon and a (step-)sister of Absalom named Tamar. Amnon lusted after her and raped her.
Absalom was enraged and killed Amnon, then fled to Geshur, the kingdom of his grandfather (on his mother's side).
2 Samuel 13:37-38:
37. Absalom fled and went to Talmai son of Ammihud, the king of Geshur. But King David mourned for his son every day.
38. After Absalom fled and went to Geshur, he stayed there three years.
King David missed Absalom and wanted to see him again - 2 Samuel 14:23,32-33:
23. Then Joab went to Geshur and brought Absalom back to Jerusalem.
...
32. Absalom said to Joab, "Look, I sent word to you and said, `Come here so I can send you to the king to ask, "Why have I come from Geshur? It would be better for me if I were still there!" ' Now then, I want to see the king's face, and if I am guilty of anything, let him put me to death."
33. So Joab went to the king and told him this. Then the king summoned Absalom, and he came in and bowed down with his face to the ground before the king. And the king kissed Absalom.
In 2 Samuel 15, Absalom tricked some Israelites into supporting him as king while David was still alive. Absalom died in 2 Samuel 18 under circumstances where David and his nephew, Joab, who was one of his commanders started parting ways before David gave the throne to Solomon.