Cleo is shown in the opening scene as the camera pans around a hotel room in Paris. She is in bed with the film's antagonist Martin Stevens when she suddenly remembers that she has a meeting with the Turkish Military Attache; Martin encourages her to stay with him but Cleo says that he has to give her a check for the Attache. Next we see Cleo getting dressed as Martin gets out of bed and begins to write a check for $18,000, but before he can finish writing he looks in a mirror and sees her pulling a gun out of her purse. Martin quickly turns around and shoots Cleo in the stomach with the gun in his pen. Cleo then gives a pained look while grasping her stomach and falls on the bed, dying soon after.
It is never revealed who Cleo works for or if she was genuinely working for the Attache, but we can assume she was not working independently, instead she must have been hired to assasinate Martin. Similarly, we do not know what her history with Martin may have been, but he did not seem broken up about shooting her in the stomach.