Zhukov was involved in Elizabeth's training and she saw him as a surrogate father. He was also Claudia's lover.
He was killed by the CIA as retribution for the Soviet-caused deaths of several FBI agents and a US scientist. Claudia encouraged Elizabeth to avenge his death by assassinating the CIA agent who ordered the killing; however Claudia eventually carried this out herself.
Zhukov is seen in a flashback giving Philip and Elizabeth their marriage certification before they are married willingly by Father Andrei.