Pete Carroll’s not dropping his side hustle -- despite landing the Raiders' head coaching job, the USC legend will continue to teach a course at the school, TMZ Sports has confirmed.

Carroll took on a role as a co-instructor this past school year ... after ending his 13-year run as the head coach of the Seattle Seahawks.

He teamed up with USC Dean of Religious and Spiritual Life Varun Soni and Adjunct Professor of Entrepreneurship David Belasco for a class called "The Game Is Life," which focuses on personal development post-grad for senior students.

The Raiders hired Carroll last week after firing Antonio Pierce ... making him the oldest head coach in NFL history.

But, his new gig won't affect his presence in the USC classroom ... at least for now. The university tells us Carroll's involvement in the class will continue.

"In our course, Dean Soni and I will hopefully help each student find their way to Win Forever," Carroll said of the teaching gig last year.

Before Pete went on to win a Super Bowl in the NFL, he was busy running the Trojans from 2001 to 2009 ... winning four Rose Bowls and a National Championship.

Once a Trojan, always a Trojan!!