Albert Barnes Commentary 2 Kings 2:9

"And it came to pass, when they were gone over, that Elijah said unto Elisha, Ask what I shall do for thee, before I am taken from thee. And Elisha said, I pray thee, let a double portion of thy spirit be upon me." — 2 Kings 2:9 (ASV)

Let a double portion of your spirit be upon me — Like Solomon, Elisha asks for no worldly advantage, but for the spiritual power to discharge his office correctly. The "double portion" refers to the share of a father's property that was the right of the firstborn son (Deuteronomy 21:17). Elisha therefore asked for twice as much of Elijah’s spirit as would be inherited by any other of the "sons of the prophets." In other words, he was simply asking to be acknowledged as Elijah’s firstborn spiritual son.