Rose attended high school at Poly Prep Country Day School in Dyker Heights, Brooklyn, where he captained the wrestling team, and graduated in 2004. He subsequently received a bachelor’s degree in history from Wesleyan University, graduating in 2008. Rose became involved in politics while a student at Wesleyan University; he worked as an intern for U.S. Senator Cory Booker while Booker was mayor of Newark, New Jersey. He later earned a master’s degree in philosophy and public policy from the London School of Economics and attended the University of Oxford.

Rose enlisted in the United States Army in 2010. He served nearly five years of active duty with the U.S. Army 1st Armored Division. In 2012–13, he was a 26-year-old first lieutenant platoon leader fighting in the War in Afghanistan, when he was wounded after his vehicle hit an improvised explosive device in northern Kandahar Province. During his service, he earned the Ranger tab, the Combat Infantryman Badge, a Bronze Star, and a Purple Heart. He serves as a company commander in the New York Army National Guard with the 69th Infantry Battalion, the second-oldest unit in the United States.

Rose ran in the 2018 Democratic Party primary for New York’s 11th congressional district against five other candidates, winning with 65% of the vote. In the general election, he faced Republican incumbent Dan Donovan and received endorsements from former President Barack Obama and former Vice President Joe Biden. Rose defeated Donovan, 52.8% to 46.8%, a win widely seen as an upset as most ratings of the race considered Donovan a slight favorite.

Rose and his wife Leigh Byrne, a fashion stylist, were married in March 2018. They reside in St. George, Staten Island. In 2020, the couple adopted a son.

In March 2019, in response to Alexandria Ocasio-Cortez’s view that Congress “could have leaned more on the larger role of other agencies before Congress decided to invade a nation without a concrete end plan,” Rose wrote to the New York Daily News:

On October 2, 2019, Rose announced his support for an impeachment inquiry against Donald Trump for his attempt to pressure Ukraine into interfering in the 2020 presidential election.

In March 2020, while serving as a member of Congress, Rose announced that he would deploy with the National Guard to assist New York City’s coronavirus pandemic response effort.

In 2020, Rose ran for reelection. He lost to the Republican nominee, State Assemblywoman Nicole Malliotakis, who represented much of the district’s eastern portion. He conceded on November 11. It is widely believed that Rose’s participation in a George Floyd protest hampered his reelection chances. The 11th district has historically been home to large numbers of New York City Police Department (NYPD) officers and their families, many of whom felt Rose’s participation was tantamount to an endorsement of defunding the police. He was also hampered by Donald Trump carrying Staten Island with 61% of Staten Island’s vote; Trump won less than 35% of the vote in the other four boroughs.