One common way for anime to introduce a new character is by having them transfer to the protagonists' school midyear. These characters can throw a wrench into the existing social order, become new partners in the fight against evil, or even become new enemies. Sometimes, they're even the protagonist, allowing viewers to observe the school environment through a fresh pair of eyes.
Who are some of the best new transfer students in anime? One great example is Homura Akemi of Puella Magi Madoka Magica, who first becomes a transfer student when her health forces her to take time off school, but then keeps doing it continuously as she goes through time loops, to ensure that she can stay close to Madoka. There's also Syaoran Li from Cardcaptor Sakura, who becomes one of Sakura's most indispensable partners, even if they don't exactly like each other at first.
Which ones are your favorites?
Kanna is a dragon from an alternate realm, so when it's time for her to transfer to a human elementary school, Tohru has to use her dragon magic to create the documents she needs to do it. Despite her non-human background, she quickly makes a friend - probably because she's so cute.
Kyo Sohma first appears partway through his second year of high school after taking time off to do martial arts training in the woods. Because he's cursed to transform into a cat whenever he makes any form of torso contact with the opposite sex, going to a co-ed school is a major adjustment to say the least.
When Yumeko Jabami first transfers to Hyakkaou Private Academy, she seems sweet and innocent. But beneath her innocent exterior lies the heart of an adrenaline junkie who loves gambling and is willing to risk everything for the next big win.
When Suzaku Kururugi first transfers to a fancy private school with an almost exclusively Brittainian population, he truly stands out. Not only is he a former full-time soldier adjusting to a part-time civilian life, he's also Japanese, a group that's heavily discriminated against by the Brittainian colonialists.