She is best known for creating roles in the Original Broadway productions of several prominent musicals during the 1960s, including Rosie in Sweet Charity and Mary in Hallelujah, Baby!, and as a regular performer on Rowan & Martin's Laugh-In from 1970 to 1972.
She also portrayed Shelley Sealy as a main cast member of the short lived TV series Glitter in 1984–1985, and performed the recurring roles of Mrs. Recinos on Becker, Mrs. Douglas on Frasier, Amanda Wilkerson on Chico and the Man, and Myrna Morgenstein in Rhoda.
She began her Off-Broadway career at the age of 19 starring in the lead role of Little Mary Sunshine and in the original production of Rick Besoyan's In Your Hat in 1957 after spending a summer performing at Camp Tamiment.
In 1970, Sharma replaced Bernadette Peters in the New York production of Dames at Sea and continued with the show for its entire run in Los Angeles.
Her performance in the show drew the attention of producer George Schlatter and led to her big break in television; landing her a part in the main cast of Rowan & Martin's Laugh-In from 1970 to 1972.