One popular trope is the team - up. Characters from Arrow and Agents of Shield joining forces to fight a common enemy. For example, Oliver Queen and Phil Coulson leading their respective teams against a new super - villain.
One idea could be that some of the Agents of SHIELD team get transported to Starling City where they cross paths with Arrow's team. They could team up to fight a common enemy like a meta - human terrorist group that has access to both high - tech weapons and ancient magic.
To write a good character interaction in an Arrow and Agents of Shield crossover fanfiction, first understand each character's personality. For example, Oliver Queen is very brooding and focused on justice in his own way. Agents of Shield characters like Coulson are more about the big picture and following S.H.I.E.L.D. protocol. So when they interact, there might be some clashes at first. But also find common ground. Maybe they both care about protecting the innocent. Let the characters learn from each other. Oliver could learn about the larger scale threats that Agents of Shield deals with, and Coulson could see the value of Oliver's more hands - on approach.
A great plot idea is a crossover centered around a new super - weapon. Maybe some ancient weapon that was lost in the Arrow - verse is found by Hydra in the Agents of Shield world. So the two teams have to work together to retrieve it before it's used for evil. Another popular one is a character - based plot. For instance, if Thea Queen discovers she has some sort of power that is related to the Inhumans in Agents of Shield. She then goes to them for help and that starts a whole series of events that brings the two groups together. Also, a plot where the two teams are forced to compete for a valuable resource, but then realize they need to work together to keep it from falling into the wrong hands can be really interesting.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfics, and you can use the search function to specifically look for Arrow and Agents of Shield crossovers. Another option is FanFiction.net, though the quality can vary more there.
Daisy Johnson from Agents of SHIELD and Oliver Queen from Arrow would also be an interesting duo. Daisy has her Inhuman powers and combat skills, while Oliver is an expert archer and martial artist. They could fight side - side in a big battle against a powerful villain.
One idea could be that Supergirl's powers are misinterpreted by Shield as a new threat. So they send some of their agents to investigate. The agents then realize she's actually a hero and they team up to fight a common enemy like a powerful alien race that's planning to invade both their worlds.
When writing an Agents of Shield crossover fanfiction, think about how the different technologies and magic systems (if applicable) will interact. If you're crossing over with a fantasy world, how will the Shield agents deal with magic? And how will the magical beings react to the high - tech gadgets? Also, focus on the character development. Let the characters from both universes grow and change as a result of their interactions. You can start with a small event that escalates into a big adventure for all of them.
First, you need to understand the characters well. For Supergirl, know her powers, her moral code, and her relationships. For Agents of Shield characters, like Coulson, Daisy, etc., study their personalities and abilities. Then, create a believable scenario for their meeting. It could be something like a shared threat or an accident that brings them together.
One great Agents of Shield crossover fanfiction is the one where they cross over with the X - Men universe. It's really interesting to see how the characters from Agents of Shield interact with mutants. The story often has some great action scenes and character development as they face new threats together.