Towards the beginning of the film, Sharon is undercover as "Kate", a neighbor of Captain America. Sharon is a young, attractive S.H.I.E.L.D. agent with skills in martial arts and weapons whose mission is to guard Steve Rogers — and not let him know it. She is guided by a strong moral compass and is not afraid to speak out when her ethics are challenged.
Sharon Carter was assigned by S.H.I.E.L.D. to monitor Steve Rogers, when Rogers arrives at his home apartment and was given the apartment opposite to his, acting as a nurse going by the name Kate. One day, Sharon Carter met Steve Rogers outside their respective apartments; after a brief chat, Rogers shyly asked Carter if she wished to join him for coffee, which she politely refused, noting she had to do her laundry. Later when Fury is attacked by the Winter Soldier she revealed her identity to Captain America.
The next day, Carter was at a meeting with Alexander Pierce, and at the end of that meeting, she came across with Steve Rogers, who ironically called "neighbor". Later, she questioned the orders from Jasper Sitwell because she did not understand why S.H.I.E.L.D. decided to hunt Captain America.
Agent Carter was present when Steve Rogers revealed that HYDRA was still alive. Also when Brock Rumlow and the STRIKE team walked to the control center to put the Helicarriers in orbit, Carter tried to stop Rumlow but he was more intelligent and manages to put the Helicarriers in orbit. After S.H.I.E.L.D. disbanded, Sharon was recruited by the CIA.
Two years after the fall of S.H.I.E.L.D., Shanon works for the CIA, being stationed at Bucharest following the fall of SHIELD.
In the comics Sharon Carter is the niece of Peggy Carter. The original comic's time jump from the 1940s was only twenty years, making it plausible that Sharon was Peggy's niece. Despite the change in timeframe, she is still Peggy's niece in the films.
In the comics, Sharon eventually fell in love with Steve Rogers becoming the primary love interest. It's implied the same thing happens in the films.