In "Turn Left" when Donna has a time beetle put on her back, who is the mysterious woman and what is her motivation?
The time-beetle (and presumably also its handler, the mysterious Fortune Teller) are identified by the Doctor as being part of the "Trickster's Brigade", a pan-species grouping of creatures and humans that are led by the Trickster, an immortal extra-dimensional alien who seems to delight in mucking around with time, both in an attempt to create disturbances and rifts through which it can enter reality and for its own perverse gratification.
THE DOCTOR: Just got lucky, this thing. It's one of the Trickster's Brigade. Changes a life in tiny little ways. Most times, the universe just compensates around it, but with you... great big parallel world!
The Trickster and his crew are seen and mentioned in a variety of other episodes within in the continuity (notably making a personal appearance in The Sarah Jane Adventures) but this particular lady only appears in 'Turn Left' and is never seen from, or referred to ever again.
Her personal motivations for helping the Trickster aren't clearly defined, but it would appear that she gains some sort of vicarious satisfaction when the time-beetle distorts reality. Suffice to say, Donna's reality distortion causes her an overload.
The FORTUNE TELLER is on the floor, curled into the corner, terrified: like she experienced all this, the whole different world, felt it, way beyond anything she'd planned