Margaret 'Peggy' Carter, aka Agent Carter, is an agent of S.H.I.E.L.D.
She can also be said to be an agent of the OSS, the French Resistance, and the Strategic Scientific Reserve (SSR).
[Note to start this off: In the Marvel Multiverse, there are a very large number of different Earths, each a tad different from the others. Each of these Earths have been assigned a number. The one known most commonly as the Marvel Cinematic Universe (MCU) is Earth-199999. The one most often seen in the comic books is Earth-616, also called the Marvel Prime Universe (MPU).
Each of the two mentioned Earths have an incarnation of Peggy Carter and both are similar in some ways and wildly different in others. There are also other Earths with their own unique version of Carter.
It is not the purpose of this entry to be the complete biographer of Agent Carter, a huge task considering the numerous Carters that there are. Marvel has an extensive database available showing extended biographies of each of these versions thus far discovered.
This page is devoted to the Peggy Carter of the MCU. The information shown below is largely from the Marvel Cinematic Universe Wiki.]
"Doctor Margaret Elizabeth "Peggy" Carter, Ph.D., was one of the most prominent agents of the Strategic Scientific Reserve during and after World War II and one of the founders of S.H.I.E.L.D.. Originally a code-breaker working at Bletchley Park, she joined the Special Operations Executive following her brother's death. Carter later joined the SSR, formed to fight HYDRA. On the mission in Germany, she saved Abraham Erskine from Johann Schmidt. The success of her mission enabled the SSR to start Project Rebirth and develop their Super Soldier Serum to make the army of Super Soldiers. During the project, she had befriended Steve Rogers, one of the project's candidates.
"In 1943, after the abrupt end of Project Rebirth and Rogers' transformation into the only Super Soldier, Carter assisted him in becoming the world's first superhero, eventually falling in love with him. After Rogers' disappearance in 1945, she continued the SSR's fight against HYDRA, capturing the last high-ranking HYDRA officer Werner Reinhardt, and continuing her service in the SSR once the War ended.
"As an agent of the SSR, Carter helped former colleague Howard Stark clear his name when he was accused of being a traitor, and later traveled to Los Angeles where she clashed with Whitney Frost over the extra-dimensional Zero Matter. She helped Stark found the new peacekeeping organization, the Strategic Homeland Intervention, Enforcement and Logistics Division, better known by its acronym S.H.I.E.L.D.. Carter eventually married an Allied soldier and became a mother of two children, though she would continue her service in S.H.I.E.L.D. during the turbulent years of the Cold War, becoming the agency's director by 1970.
"By the beginning of the 21st century, Carter retired and saw her great-niece, Sharon Carter, follow in her footsteps. During her retirement, a young Rogers was pulled from the ice and found to be alive, but by this time she had been diagnosed with Alzheimer's disease and struggled to recognize him. She died peacefully in her sleep in 2016."