It could change his relationships. If the device has some unique function like showing a person's true intentions, it might make Harry more cautious about who he trusts. On the other hand, it could also help him strengthen his bonds with his true friends. For instance, if it can record and replay memories, he could share more intimate and important moments with Ron and Hermione, deepening their friendship even further.
It could be a magical time - traveling device. Maybe it allows Harry to go back in time to change certain events in the wizarding world, like preventing some of Voldemort's early atrocities.
If the device in the fanfiction is a time - traveling gadget, it could completely transform Harry's life. He could go back in time to learn from the founders of Hogwarts, understand the origin of certain dark magic, and use this knowledge to prevent future disasters in his own time. It would also give him a chance to meet his parents and gain a deeper understanding of his own heritage.
It could be Dumbledore. He always has a knack for providing Harry with useful tools. Maybe he found this device during one of his travels and thought it would be beneficial for Harry's growth as a wizard.
He could become more confident. With the new resources from his inheritance, he feels more secure in his place in the wizarding world. For instance, if he inherits a lot of gold, he doesn't have to worry about financial problems at Hogwarts.
There's a possibility that it's a mysterious figure from a different wizarding school. This person could have heard of Harry's reputation and journey. They might give Harry the trivet as a sign of alliance or as a test. They want to see how Harry will use this strange object. Maybe this figure is from a school that has a different approach to magic, and the trivet is a symbol of that different magical culture.
It could change his life by giving him a new form of magic. For example, he might be able to combine the power of the stand with his existing magic, making his spells more powerful.
His living conditions would change drastically. Instead of living in the wizarding world, he'd be in palaces. He'd have servants and all the luxuries that come with royalty. His friends at Hogwarts would be replaced by new acquaintances in the royal circle. He'd have to adapt to a very different set of rules and expectations.
It could be a group of fans who collaborated to write this fanfiction. They might have different ideas about what 'receives a tri' means and combined their creativity to come up with a story. Maybe they met in an online Harry Potter fan community and decided to work together on this project.
Perhaps 'tr' is a time - turning relic. Harry Potter gets it and is faced with the moral dilemma of whether to use it to change past events. He might consider using it to save his parents, but then realizes the potential consequences of messing with time. This could lead to a whole adventure where he has to make difficult decisions and also face the Time - Turner's side - effects, like being in two places at once in a confusing way.
Well, it could be that Harry Potter gets a magical item from the Trival in the fanfiction. Maybe it gives him some new powers that he uses to fight against Voldemort in a different way.