Allah (swt) says:
"(And We guided) Ishmael and Elisha, and Jonah and Lot, and to all We gave favour above the nations." (6:86)
"And mention Ishmael and Elisha, and Dhul-Kifl, and they were all of the best." (38:48)

Elisha came after Elias. He called his people to the way of Allah, and followed the Laws and Shariah revealed to Elias, till he passed away.It is said that he was the cousin of Elias and he was also in hiding with him in the cave, where he hid for the fear from the king of Baalbek. When he came out of his hiding, Elisha also went with Elias to his people. When Elias died, Elisha overtook his mission from him, and was sent by Allah as His Prophet to his people.