If Viper is Maverick's mentor, for the most part, it is Lieutenant Commander "Jester" Heatherly that does a lot of the teaching. He's at the helm during the first day of instruction, and he's usually in front of the class. He's almost always up in the air with the guys as well, and he's also usually the one who provides Maverick with more direct coaching, criticism, and the like (even though Viper is the more important presence).
There isn't a whole lot of depth to Jester, and he doesn't really change too much throughout the film. In a lot of ways, he handles all the day-to-day stuff for Viper and Top Gun, and he's almost reduced to the role of "highest ranking guy who is not actually the head honcho."
He has a deep, imposing voice, which makes him kind of scary, and he's definitely gruff and a man of few words, a true military man. Michael Ironside, the actor who plays Jester, really looked the part. In a famous incident, an actual enlisted member of the Navy was running and stopped short and saluted Ironside (who was in costume), thinking he was an actual officer.