In such a fanfiction, it could lead to some major plot twists and character developments. The Avengers' loyalties and actions would likely be completely different.
Definitely the Avengers members like Captain America, Iron Man, Thor, Hulk etc. would be main characters as they are the core of the Avengers. On the Hydra side, characters like Baron Wolfgang von Strucker could be prominent. Also, there might be some original characters created specifically for the fanfiction, perhaps a Hydra scientist who is behind a new and dangerous experiment targeting the Avengers.
One idea could be a crossover where Hydra discovers the wizarding world in the Harry Potter universe and tries to use magic for their evil purposes. The Avengers somehow get wind of this and team up with Harry Potter and his friends to stop Hydra. Maybe they have to battle magical creatures that Hydra has corrupted with dark magic.
The Avengers would likely be very protective of her at first. For example, Thor might use his strength to keep her safe from any immediate threats. Iron Man could use his technology to check if she has any tracking devices on her or if she's been poisoned by Hydra.
A really interesting one is 'Avengers vs Hydra: A New Perspective'. It presents a different view of the age - old conflict. Instead of the usual fight, it explores the idea of some Avengers having a more nuanced view of Hydra and how that affects their actions and the overall dynamic within the team.
Fanfiction explores it in many ways. For example, some might show a reluctant alliance between an Avenger and a Hydra operative for a common goal. This shows that the relationship is not always black and white.
Perhaps in the 'avengers of hydra fanfiction', Hydra has developed a new super - weapon that can neutralize the Avengers' powers one by one. The story could follow the Avengers as they scramble to find a way to counter this weapon while also dealing with Hydra's attacks on various cities. Or, there could be a plot where a powerful Hydra agent uses magic to possess some of the Avengers and make them do Hydra's bidding, and the remaining Avengers have to find a way to break the spell.
The Avengers would be in a state of panic and fury. Captain America would likely lead the charge to find Tony. He'd use his military strategy skills to plan a rescue mission. Thor might use his godly powers to track down any signs of Tony's whereabouts. Black Widow and Hawkeye would be on the lookout for any Hydra agents or informants. Hulk could be a wildcard. He might be uncontrollably angry and ready to smash anything in his path to get to Tony.
Perhaps there is a magical artifact in the Harry Potter universe that Hydra believes can give them ultimate power. They send agents to steal it, but the Avengers also learn about it. The two groups end up in a race to get the artifact, and along the way, they both have to deal with the magical defenses and creatures in the wizarding world. Harry Potter and his allies then have to decide who to trust - the Avengers who seem to have good intentions but are from a different world, or Hydra which is clearly evil.