Perhaps a rogue ninja from another village who sees Naruto as a threat. This ninja could target Anko and Naruto during their training. He might be jealous of the Hidden Leaf's strength and think that if he can stop Naruto from getting stronger under Anko's teaching, he can weaken the Leaf Village. He could be a skilled fighter with unique abilities that pose a real challenge to Naruto and Anko.
There could be an internal antagonist within the Hidden Leaf Village itself. Someone who doesn't like the idea of Anko teaching Naruto. Maybe this person is jealous of Anko or has some ulterior motives. They could try to undermine Anko's teaching by spreading false rumors about her or trying to get Naruto removed from her care. This would create conflict not only between Naruto and this antagonist but also between Anko and the village authorities if they start to believe the false rumors.