It could be a rogue ninja from Orochimaru's former experiments. This ninja might hold a grudge against Anko for betraying Orochimaru and decides to target her. Naruto would then have to face this powerful and vengeful enemy to save Anko.
Maybe a resurrected minion of Orochimaru that was thought to be dead. This minion blames Anko for Orochimaru's downfall in a way. It has some dark and powerful jutsu at its disposal. Naruto would have to dig deep into his own power reserves and new jutsu he's developed to defeat this minion and rescue Anko.
Perhaps Anko is trapped in a genjutsu and Naruto uses his own experience with breaking free from illusions to save her. He could sense her distress and use his chakra to disrupt the genjutsu, freeing Anko. This would show Naruto's growth and his ability to help those in need, even a more experienced ninja like Anko.
One possibility is that Anko is poisoned during a mission. Naruto, having learned some medical ninjutsu from Tsunade, uses his skills to find an antidote and save her. He might have to search far and wide, facing various challenges along the way.
In a 'naruto saves anko' fanfiction, Naruto might find Anko in a dangerous situation like being trapped in a genjutsu by a rogue ninja. Naruto, with his strong will and Uzumaki chakra, could break the genjutsu and save her. He'd then comfort her and they might form a stronger bond, leading to Anko having more faith in the new generation of ninja.
It could be Orochimaru. He might be interested in Ino's unique abilities, like her mind - control jutsu, for his own evil experiments. So he kidnaps her, and Naruto has to fight against Orochimaru's snake - like techniques to save Ino.
A powerful and mysterious organization could be the main villain. They have been secretly manipulating events in the ninja world for years, and now they plan to use a powerful weapon to destroy all the hidden villages and take over the world. Naruto has to expose and stop them.
Naruto could save Anko from a rogue ninja who infiltrated the training grounds. He'd use his ninja skills and his determination to keep Anko safe.
It could be a young ninja from a minor clan who has been overlooked in the regular training regime. Anko sees potential in this ninja and decides to take them under her wing.
Perhaps a rogue ninja group that has a vendetta against Anko. When she forms this new family with Naruto, they target the whole family unit to get back at her. They might see Naruto as a way to get to Anko or vice versa, and constantly attack and create chaos for them.
It could be a rogue ninja from a hidden village who has a vendetta against Konoha. This ninja might target Kurenai and Anko specifically because of their skills and knowledge, and Naruto gets in the way while trying to protect them.
Perhaps it's a group of mercenary ninjas. They've been hired by someone who has a grudge against Zabuza. They see Zabuza as an easy target when he's alone or vulnerable, but Naruto shows up to spoil their plan.