At an age when most people retire, Mickey Drexler is starting a new job. The former Gap Inc. and J.Crew Group boss is taking over as chief executive officer of Alex Mill, a clothing brand his son started.

Mr. Drexler made Gap T-shirts and khakis cool in the 1990s and spearheaded a turnaround at J.Crew. But he left both companies amid prolonged sales slumps. Now, at 76 years old, he is diving back into the business at a time of upheaval, as brands emerge from the Covid-19 crisis and continue to grapple with the shift to e-commerce.

“I’ve been through many non-fun periods in my career,” Mr. Drexler said in a recent interview. But he said he is having more fun now than ever because the company is small enough that he can focus on the details, down to the color, style and buttons of every garment. “I never want to retire,” he said.

His son Alex Drexler founded Alex Mill in 2012 as a maker of men’s shirts sold at luxury stores such as Barneys New York. After Mickey Drexler stepped down as J.Crew’s CEO in 2017, he made an investment in the company, became an adviser and introduced his son to Somsack Sikhounmuong, who had served as J.Crew’s design chief.

The Alex Mill store in Manhattan’s SoHo area. Mickey Drexler’s son Alex founded the company as a maker of men’s shirts.

The Alex Mill store in Manhattan’s SoHo area. Mickey Drexler’s son Alex founded the company as a maker of men’s shirts.

In 2018, Alex Drexler and Mr. Sikhounmuong relaunched Alex Mill with broader collections for women and men and focused on selling directly to consumers through its website and a bricks-and-mortar store, although the brand is also sold by other retailers, including Nordstrom Inc. and Net-a-Porter.

This month, Mickey Drexler is making another investment in the closely held brand, through Drexler Ventures, his investment fund. He declined to specify the amount but said it was “significant.” He is the largest shareholder, followed by his son and Mr. Sikhounmuong, who will both hold the title of co-founder.

Mickey Drexler casts a larger-than-life shadow, and that hasn’t always been easy for his son, who says that at times he felt sidelined. “If I had to do it over again, I would have been a lot more sensitive,” Mickey Drexler said. “I should have been a father first and a business associate second.”

The two sought help from someone Mr. Drexler calls a therapist and his son calls a business coach, who mitigates disagreements.

Alex Drexler and Somsack Sikhounmuong relaunched Alex Mill in 2018 with broader collections for women and men.

Alex Drexler and Somsack Sikhounmuong relaunched Alex Mill in 2018 with broader collections for women and men.

Mickey Drexler said he has learned from the sessions. The two recently disagreed about a men’s anorak jacket for a coming collection: The father didn’t like it, but the son convinced his father that it added something special to the line. “He said, if I believe in it, he believes in it,” said Alex Drexler, who is 43.

Striking out on his own was important to the younger Mr. Drexler. He got his start in fashion working for clothing brands Steven Alan and Gryphon, before launching Alex Mill. He said he is happy his father is involved in the company because of the leadership and vision he brings.

It helps that father and son have different areas of expertise. Alex Drexler is more involved with marketing, partnerships and production. His father is more focused on the products and customer experience. Mr. Sikhounmuong oversees design.

Mickey Drexler is boosting his investment in Alex Mill and is its largest shareholder.

Mickey Drexler is boosting his investment in Alex Mill and is its largest shareholder.

The two Drexlers also have different management styles. “Mickey feeds off being around people,” said his son. “I prefer smaller meetings, and sticking to one agenda at a time. Mickey likes to throw lots of ideas out there.”

At Alex Mill’s office, Mickey Drexler holds ad hoc focus groups consisting of the company’s 20 or so employees. He sits at a table surrounded by his staff and peppers them with questions about which styles and colors they like best.

One recent discussion centered on a cashmere cardigan. Mickey Drexler was concerned that certain colors, including bright green and burnt orange, wouldn’t sell well. Some employees argued that the colors added novelty, but ultimately they were dropped from the line.

“He wants us to push back,” said Rose Anderson, the company’s social media manager. “Part of being on this team is having the guts to speak back to him.”

Mickey Drexler is fastidious about every detail, from a dress’s French seams to the backer buttons on a men’s work shirt that prevent the buttons from popping off. “If you have a strong conviction, as I have, you push for it no matter what the group thinks,” he said.

If Gap under Mickey Drexler stood for American optimism and J.Crew sold preppy clothes with a twist, then Alex Mill is updated classics, such as $150 Oxford button-down shirts and $125 cardigan sweaters. One of its signature items is a jumpsuit, the inspiration for which came while Mr. Sikhounmuong was rummaging around in a Los Angeles vintage shop.

Mickey Drexler said Alex Mill is small enough that he can focus on details down to the color, style and buttons of every garment.

Mickey Drexler said Alex Mill is small enough that he can focus on details down to the color, style and buttons of every garment.

Photo: Gabby Jones for The Wall Street Journal

Mickey Drexler is tackling a new challenge after the pandemic upended his industry—J.Crew filed for bankruptcy last year and has emerged under new owners—and at a time when the playbook of his past successes may no longer apply.

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“The business used to be solely about having the best product,” said Andrew Rosen, who founded the clothing brand Theory with designer Elie Tahari. “Today, it’s also about marketing.”

Mickey Drexler is the first to admit that social media isn’t his area of expertise. “I still believe in word-of-mouth,” he said. “That’s the 1940s way.” This is one area where he depends on his son. “Alex is as good as it gets with Instagram and email marketing,” he said.

Despite the growing reliance on data and analytics as more shopping has shifted online, Mickey Drexler still relies on his gut instinct and intuition in determining what shoppers will want.

“I use data,” Mr. Dexler said. “It’s called a sales report.”

In an era of data and analytics, Mickey Drexler relies on his gut instinct and intuition in determining what shoppers will want.

In an era of data and analytics, Mickey Drexler relies on his gut instinct and intuition in determining what shoppers will want.

Write to Suzanne Kapner at Suzanne.Kapner@wsj.com