In the United States, she performed at Yale Repertory Theater under the direction of Andrzej Wajda in White Marriage (1977) and played "Mama" in the Academy Award winning film, Molly's Pilgrim (1985).
Since then, Terra Incognita produced its Ophelia Tapestry at WAX and Construction Company in 2004; Manhattan Theatre Source hosted a workshop of Terra’s interpretation of Shelagh Delaney’s A Taste of Honey in 2006; a workshop of Pebble-and-Cart Cycle: one-line tragedies, Parts I and II performed at Dixon Place in 2008; and limited-engagement runs of Pebble-and-Cart Cycle: one-line tragedies, Parts I-III ran at the new Dixon Place and at the Capital Fringe Festival in Washington, D.C., in 2009.
The company’s installation-performance piece Hair of Sand appeared first in 2009 at both Dixon Place and through the chashama Windows Program, supported by a grant from the Lower Manhattan Cultural Council.
As of 2002 she taught acting in New York City at Michael Howard Studios and Hunter College, and in New Haven, Connecticut at Yale University, where she received a Roothbert Fund Award for Innovative Teaching.
Over 30 years, Klimovitskaya developed a unique acting approach known as "Kinetic Mind Practice" which she has applied at institutions such as New York University, Brooklyn College, Stella Adler Studio, and the National Shakespeare Conservatory.