His role could be that of a teacher. Since he doesn't have emotions clouding his judgment, he could teach the Fairy Tail members about self - control and the importance of thinking rationally. He could show them how to use their magic more effectively without being carried away by emotions like anger or pride. He might also introduce them to some ninja techniques that are based on discipline rather than raw emotion.
He could be a mentor. Naruto has learned a lot throughout his journey in his own world, and he could pass on that knowledge. For example, he could teach about friendship and the importance of never giving up. His experience with fighting powerful enemies could give the Fairy Tail members new strategies.
A Naruto swordsman in a Fairy Tail fanfiction could be a mentor. He could teach the Fairy Tail members about different sword - fighting styles and the importance of discipline in combat, which are values often emphasized in Naruto. His presence would also add a new layer of diversity to the guild, as his skills and abilities would be different from the traditional magic - based skills of Fairy Tail.
Naruto could be a protector. Just like he protected Konoha in his own world, he would protect Mavis and the Fairy Tail guild. His combat skills would be a great asset.
His role could be as a bridge between different worlds or groups. Since he comes from the Naruto universe, he could introduce new ideas and ways of fighting to Fairy Tail. He might also be the one to try and unite different factions within the guild or even between different guilds. His status as an S - Class mage would give him the influence to make these kinds of changes and connections.
He could be a powerful ally. Given his strength, he could easily help the Fairy Tail guild in battles against powerful foes like Acnologia or Zeref.
It might be that in this fanfiction, the writer wants to explore a different side of Naruto. By making him emotionless, they can create unique interactions with the Fairy Tail characters. For example, his lack of emotion could contrast sharply with Natsu's fiery personality, leading to interesting story developments.
It could work by making Naruto a more mysterious and brooding character. In Fairy Tail, there are many characters with different personalities. An emotionless Naruto would stand out. He might be more focused on achieving his goals without being distracted by emotions. For example, he could be on a mission to find a way back to his own world and his lack of emotion helps him stay determined.
One possible plot could be that Naruto is transported to the Fairy Tail world and is somehow stripped of his emotions during the process. The Fairy Tail wizards then have to figure out how to send him back while also trying to restore his emotions. Along the way, Naruto's lack of emotion might cause him to make some uncharacteristic decisions that put everyone in danger.
He could be a sort of enigma. His role might be that of a lone wolf, going on solo missions that require stealth and quick decision - making without the interference of emotions. For instance, he could be sent to infiltrate a group of Hollows or a rogue Soul Reaper faction.
One possibility could be that a main character, perhaps Natsu, is somehow reborn without emotions. He would then go through the world of Fairy Tail in a very different way. For example, he might not be as eager to fight for his friends because he doesn't feel the passion or loyalty he once did. This could lead to a lot of conflict within the guild as they try to figure out how to bring back the old Natsu.