To carry out Kronsteen's plan -- to kill protect, then kill, 007 and the girl, steal the Lector, and embarrass MI6 with their affair -- through her field agents, Grant and Tatiana, whom she recruits; to kill Bond when everyone else fails.
After defecting from the USSR (SMERSH), she becomes # 3 in S.P.E.C.T.R.E. and its head of operations.
Tatiana decides where her real loyalties are and pulls the trigger.
Rosa Klebb is like most of the major characters in 'Russia,' a spectacular example of a complex character. She is a female defector from the USSR but contrary to our expectations, she doesn't flee to the arms of liberty, but to the yoke of evil. Almost certainly a lesbian, she is the first in the series, but not the last, and she clearly takes an 'interest' in Tatiana.
Klebb's strength lays largely in her parochial demeanor. She runs a tight ship, able to pick an agent from her training camp, sinister because she is ruthless and efficient. She has no need to act extravagantly or personally, only to get the job done -- the hallmark of S.P.E.C.T.R.E. in its heyday. Even when she encounters Bond face to face, she tries to escape his notice, not flaunt her superiority, and flies to attack when she is pressed to the wall.
As a whole, Klebb is interesting because of all the tidbits we get from her, and the surprising believability of her character, in spite of her extraordinary background. Nevertheless she does suffer from disappearing for the majority of the film. Yes, she's hands off, but as a character she loses memorability points for that.
Unfortunately, she fails in her overconfidence. This may be either a cause or an effect of her hands-off approach. She has complete faith in Grant, who is apparently a new operative -- a foolish decision no matter what his background. Additionally, she reads up about the sexual history of Tatiana, but never seems to count on her loyalty (either for Russia or Bond), a failure which brings about her own death. In any case, she is a truly solid nemesis for 007, even if he himself never realizes it.