Claudia's career in the KGB has spanned decades. Early in her relationship with the Jennings, she arranges for them to be kidnapped and tortured, in an attempt to ferret out a KGB mole. When Elizabeth discovers this, she beats Claudia severely.
Despite her fraught relationship with Elizabeth, by 1987, Claudia has joined her in training Paige on the basics of spy work. She also teaches Paige how to cook several Russian dishes, shares her love of Tchaikovsky, and exposes her to Russian movies. She tells Paige her family was killed in World War II and she served at Stalingrad.
Elizabeth and Claudia part ways when Elizabeth learns Claudia has used her in a ploy to oust Mikhail Gorbachev. Claudia appears to have successfully escaped the US, but her ultimate fate is unclear. After leaving her parents on the train before it crosses the Canadian border, Paige returns to Claudia's apartment alone and drinks the vodka from her freezer.