Bill Belichick’s makeover at North Carolina is starting to look less like a rebuild of the football program and more like a continuing tabloid drama.

The 73-year-old coach whose relationship with 24-year-old Jordon Hudson has kept Chapel Hill buzzing is poised to hire Bobby Petrino, a coach once fired in disgrace over an affair with a much younger female staffer.

Under normal circumstances, Mr. Petrino’s hiring as UNC’s new offensive coordinator would be a footnote given his indiscretion happened 13 years ago. But his return to a high-profile college job comes amid a climate in college athletics that is increasingly sensitive to issues of power, conduct and accountability.

Mr. Petrino, 64, arrives at UNC just weeks after Michigan dismissed coach Sherrone Moore for an inappropriate relationship inside his program, a scandal that escalated into criminal charges and national headlines that embarrassed the program and the university.

The Michigan case is relevant because Mr. Petrino joins Mr. Belichick’s staff from a second stint at the University of Arkansas where he was fired as the head coach in 2012 after a motorcycle accident led to revelations of an extramarital affair.

Married and a 51-year-old father of four at the time, Mr. Petrino tried to conceal his relationship with 25-year-old Jessica Dorrell, a former Razorbacks volleyball player, who worked for the Razorbacks Foundation. Mr. Petrino hired Ms. Dorrell, who was riding with him at the time of motorcycle accident, to be the student athlete development coordinator for the school’s football program.

It’s difficult not to link Mr. Petrino with Mr. Moore, who not only lost his $5 million a year job, but also faces charges of home invasion, stalking and breaking and entering stemming from events connected to the “intimate” relationship he had for “a number of years.”

Mr. Moore was fired from his head coaching duties when the woman confirmed the relationship. Later that day, he allegedly “barged” his way into the woman’s apartment and grabbed a butter knife and some scissors and threatened his own life, telling her, “My blood is on your hands.”

To his credit, Mr. Petrino apologized for his actions and has rebuilt his coaching career. He served as the head coach at Western Kentucky before making stops at Louisville, and Missouri State. More recently, he served as an assistant coach at UNLV, Texas A&M and Arkansas.

He became the Razorbacks interim head coach after Sam Pittman was fired after a 2-3 start. Mr. Petrino went 0-7 as the head coach, losing four games by one score.

Still, given Mr. Petrino’s age, and checkered past, Mr. Belichick’s message is unmistakable. The six-time Super Bowl champion intends to fix North Carolina’s offense under his own terms, optics be damned.

Mr. Belichick fired offensive coordinator Freddie Kitchens earlier this month after the Tar Heels finished the season with a disappointing 4-8 record.

North Carolina scored 20 or fewer points in seven of the last nine games when the Tar Heels had an opportunity to become bowl eligible. Carolina lost five games by 16 or points or more and finished at the bottom of the ACC in several statistical categories.

Mr. Petrino is noted for a tempo-drive spread system and developing quarterbacks. He coached Heisman Trophy-winning quarterback Lamar Jackson for three seasons in Louisville.