In a third-floor workshop off the Corso Magenta, where the light comes through tall windows onto six cutting tables, Ernesto Bramante has been making suits since 1971. He is 74. His senior coatmaker is 68, his trouser maker 71. The youngest person on the floor, an apprentice named Sofia Ravizza, is 24, and she is the first person under 40 the workshop has hired since 2009.

“I have 340 customers waiting for a first fitting. Some have been waiting two years,” Mr. Bramante said, running a thumb along a chalk line on a length of grey flannel. “I could take 40 more a year if I had the hands. I do not have the hands.”

Milan’s bespoke tailoring trade, a cluster of perhaps 60 workshops that has supplied the city’s industrialists, bankers and, increasingly, visitors from Asia and the United States since the 19th century, is in the odd position of being both booming and dying. Demand for hand-made clothing has risen sharply since the pandemic, part of a broader turn toward the slow and the traceable, and a Milanese bespoke suit, which starts at about 5,000 euros, is now a destination purchase. But the craft takes 7 to 10 years to learn, pays an apprentice perhaps 1,100 euros a month in a city where a room costs 800, and has not been seriously taught in Italian vocational schools for a generation.

The trade’s own count, compiled by the Milanese tailors’ association, puts the average age of its 410 working artisans at 63. Thirty-one of them are over 75. The association projects that without new entrants, the city’s capacity will fall by half within eight years.

“For 40 years we told young people that this was no life, that they should go to university, and they listened,” said the association’s president, Anna Maria Scotti, whose family workshop closed in 2019 when her father retired without a successor. “Now we are begging them to come back, and they ask why they should believe us.”

The answer the trade has come up with is a school. The Scuola di Sartoria Milanese, which opened in September in a former textile warehouse in the Bovisa district, takes 24 students a year for a three-year course that combines classroom instruction with paid placements in member workshops. It is funded by a levy on the workshops themselves, a grant from the Lombardy region and donations from four luxury groups that depend on the same shrinking pool of skills for their own ateliers. Tuition is free. Students receive a stipend of 900 euros a month.

Ms. Ravizza, who studied fashion design at a polytechnic and found the industry jobs on offer were “mostly Excel,” is in the first class. “I wanted to make a thing with my hands that someone would wear for 20 years,” she said, pinning a sleeve. “I did not know this existed. Nobody my age does. That is the actual problem.”

Mr. Bramante, who sits on the school’s board, is cautiously hopeful. He has told Ms. Ravizza she can have the workshop in 10 years if she wants it. “She says she will think about it,” he said. “That is more than anyone has said to me in 15 years.”