A common theme is family and clan loyalty. Since the Sarutobi are an important clan in the Naruto universe, many OC fanfictions explore how the original characters uphold the values and traditions of the clan. Another theme is the pursuit of power. OCs often strive to become strong ninjas, just like the well - known Sarutobi characters in the original series.
Training and growth is also a frequent theme. The female OC might be shown going through rigorous ninja training, developing her skills, and facing challenges along the way. This often includes her learning from the more experienced Sarutobi members or surpassing their expectations.
One possible fanfiction could be about an OC (original character) who is a student of Hiruzen Sarutobi. This OC has always heard tales of Minato Namikaze's heroics. The story could involve the OC getting into a difficult situation, perhaps a dangerous mission, and drawing inspiration from the skills and courage of Minato. Hiruzen, as the wise teacher, could guide the OC in learning from Minato's example. For example, the OC might be struggling with a new jutsu, and Hiruzen tells them how Minato mastered a similar one with his determination and innovation.
One great Sarutobi OC fanfiction is 'The Hidden Sarutobi'. It focuses on an original character within the Sarutobi clan who has unique abilities and has to face various challenges in the Naruto world. Another is 'Sarutobi's New Hope' which explores the story of an OC who befriends the Sarutobi family members and gets involved in important events in the village.
You can try fanfiction websites like Archive of Our Own (AO3) or FanFiction.net. These platforms usually have a wide range of fanfictions, including those related to Sarutobi OC female. Just use the search function and type in relevant keywords.
Obviously Naruto would be one of the main characters interacting with him. Naruto would look up to Sarutobi as a mentor and a source of knowledge. Their interactions could range from training sessions to deep conversations about the future of the village.
In this fanfiction scenario, Naruto might learn unique chakra control techniques from Sarutobi. Sarutobi, being an experienced ninja, could teach Naruto how to better manage his large chakra reserves. This would lead to Naruto being able to perform jutsus more efficiently and with less waste of chakra.
I really like 'Sarutobi's Unseen Trials'. In this fanfiction, it focuses on the political aspects that Sarutobi had to deal with in the Hidden Leaf Village. It gives a new perspective on his leadership and the difficult decisions he had to make.
Perhaps in this fanfiction, Sarutobi is trapped in a genjutsu created by a rogue ninja. Naruto, being highly resistant to genjutsu due to his Uzumaki blood, manages to break into the genjutsu world. There, he has to fight his own inner demons as well as the rogue ninja's illusions to free Sarutobi.