The Daily Beast’s new leaders will do a round of voluntary buyouts intended to cut costs by $1.5 million, in one of their first major moves to try to revitalize the flagging digital tabloid.

The new leaders, Joanna Coles and Ben Sherwood, both media veterans, joined the company in April in exchange for an equity stake in the business. Barry Diller’s company, IAC, maintains control of the publication.

The Daily Beast’s union told its members in a memo this week that workers would have until June 14 to apply for a buyout, after which the publication would accept applications “in reverse seniority order until they meet their $1.5 million threshold.”

Decisions on additional applications beyond that threshold would be up to the company, and there would be “a moratorium” on further layoffs until the end of the year, according to the union’s memo. The cuts are not targeting any particular coverage area.

About 10 to 15 members of The Beast’s unionized editorial staff — about a third — are expected to take a buyout, according to two people familiar with the discussions. Mr. Sherwood and Ms. Coles are also planning to make cuts beyond the unionized staff.

A spokeswoman for The Daily Beast said the buyouts were part of a plan to reduce spending, increase revenue and put The Beast into a “healthy and sustainable financial position.”

“Everyone in digital media is facing tough choices,” the spokeswoman said. “These buyouts are especially hard because we know some talented and valued colleagues will decide to leave next month.”

The publication has historically lost millions of dollars annually, according to a person familiar with the matter, who said the company was planning to reach break-even at some point next year.

Ms. Coles, who is the chief creative and content officer, and Mr. Sherwood, the chief executive and publisher, have looked for other ways to cut costs, including using less office space. The Daily Beast is also moving away from its in-house publishing technology to one developed by another company, and it is bringing aboard digital subscription specialists to make the subscription process less cumbersome.

The Daily Beast’s audience has decreased substantially in recent years, according to two people familiar with the matter. It has about 100 workers.

Mr. Diller had looked at selling The Beast. He ultimately decided on the partnership with Ms. Coles and Mr. Sherwood as a turnaround effort.