The StarS and Lightning Teams in StrikerS consisted of two experienced instructors and two students.
Robin Mask and his disciple Warsman form the Choujin Master/Student Combo in Kinnikuman's Dream Tag Team Touranment arc. Though the two are on more equal footing than most examples.
History's Strongest Disciple Kenichi: When ever Kenichi gets thrown into one of these with any of his masters (and it happens a lot), it's not because he's needed, its because the masters want to train him by having him fight their opponents' disciple.
Puella Magi Madoka Magica: Across its various spin-offs and timelines Mami has been the master to three different students: Kyouko, Sayaka in A Different Story and Madoka in the main series' original timeline. She taught each one the basics of Magical Girl life and fought alongside them against witches.
Granny Weatherwax and Tiffany in A Hat Full of Sky. Nanny Ogg and Tiffany in Wintersmith. Interestingly, not Tiffany's official witchcraft teachers, who are helpful, but don't exactly fit the trope. Other times the witches fall into The Hecate Sisters ensemble.
The Doctor and his companions, although less so with the reboot's tendency for younger (-looking) Doctors. Also, there's never any suggestion of them filling his shoes, for obvious reasons.
With a few almost exceptions - Romana leaves to serve a similar role in another universe, while the never completed plot arcs may have had Ace eventually becoming a Time Lord. Sarah Jane also gained a similar role in her own spin-off, complete with apprentices of her own.
A staple of Highlander, where veteran immortals would train newborns.
The MS T3k episodes "Master Ninja" and "Master Ninja II" feature a team like this, in the form of Lee Van Cleef and Timothy Van Patten, as does "The Master," the TV show from which the movies were hastily spliced.
Kickin' It: Jack and Rudy entered a tournament where each team had to be this.
Buffy and Giles in Buffy the Vampire Slayer, the television adaptation of the film mentioned above. The job of a Watcher is to train and look after The Slayer, though the Watcher doesn't always engage in combat.
In Star Wars: The Old Republic, if you play as either a Jedi or a Sith (regardless of the class), one of your companions will be your apprentice. Sith Inquisitors get two of them: the Light Side-leaning Ashara and the very Dark-Sided Xalek.
Disgaea has an entire mechanic where characters can serve as mentors to other characters they were used to create with useful advantages for both (for example masters can use the skills of any apprentices that are nearby).
The Kung Fu chapter of Live A Live has the master and his surviving student seeking revenge together.