One possibility could be that Hermione is going through a difficult time at Hogwarts, perhaps with her studies or facing some sort of social ostracism. The older man, who might be a wise teacher or a kind-hearted wizard from the community, offers her words of wisdom. He could share his own experiences of facing similar difficulties when he was young, which makes Hermione feel less alone.
Perhaps an older wizard from the Ministry of Magic who has noticed Hermione's great potential and talent. He could be someone who has seen many young witches and wizards struggle and wants to make sure Hermione doesn't get lost in her own doubts. He would use his experience in the wizarding world to comfort and guide her.
Once, an older man was walking in the countryside. He came across a duck that was stuck in a muddy area. The old man, with his gentle hands, freed the duck. The duck didn't fly away immediately but stayed for a moment as if to thank the man. From that day on, whenever the old man passed by that area, he would look around hoping to see the duck again, and sometimes he did, which always made him smile.
In the fanfiction, Hermione and her older sister could have a complex relationship. Maybe the sister is overprotective, constantly looking out for Hermione at Hogwarts, especially with all the dangerous situations she gets into. The sister could also be a bit jealous of Hermione's academic success and magical abilities, which could lead to some sibling rivalry.
One reason is the contrast in experiences. Older characters have seen more of the wizarding world, and Hermione's thirst for knowledge makes it interesting to see her interact with someone who can offer a different perspective. For example, in many such fics, an older man might introduce her to forgotten spells or ancient magic.
One common trope is the 'forbidden love' angle. Since it's an older man, it goes against the social norms in the wizarding world. Another trope is the 'mentor - mentee' relationship that often turns into something more. The older man might start as a guide to Hermione, like in magic studies, and then his feelings change.
In many fanfictions, Harry might comfort Hermione by simply being there for her. He could sit quietly beside her while she's upset, offering his silent support. Maybe he'll hold her hand gently to let her know she's not alone.
One popular 'Hermione needs an older man' fanfiction is 'The Time Turner's Influence'. In this fic, an older wizard from a different era becomes Hermione's mentor and more. It delves into how their age difference creates a unique dynamic. Another is 'Older Eyes on Hermione' which focuses on an older Order of the Phoenix member taking an interest in her growth, both magically and personally.
Often, the older man is portrayed as very sophisticated. He might be highly educated, perhaps a well - respected wizard in the magical community. For example, he could be a renowned scholar or a powerful figure in the Ministry of Magic. This makes him an attractive alternative to Ron in the eyes of some fanfiction writers who want to show Hermione being drawn to a more worldly and accomplished partner.
One common theme is redemption. Draco often needs to redeem himself after his actions during the war, and Hermione's comfort is a step in that process. For example, in many stories, he has to face the consequences of his family's loyalty to Voldemort, and Hermione helps him see a different path.
One common theme is friendship. Hermione and Ron have a deep friendship, and in these fics, that friendship is shown as a source of comfort. For example, Hermione might use their shared memories to cheer Ron up.