Well, Hanzo might come back for revenge. So Naruto and Konan would have to be on their guard. They could start training together to get stronger in case Hanzo returns with a more powerful force. Konan could teach Naruto some of her unique skills with paper, and Naruto could show her some of his new Rasengan variations. In the process, they could form a strong bond, not just as allies but also as friends. This new friendship could lead to new story arcs where they team up to face other threats in the ninja world.
Konan might decide to join Naruto in his adventures. She could use her paper techniques to help Naruto in future battles.