Clinging is a physical, exotic advantage, described in Basic Set, p. 43. It has the special limitation Specific. It is referenced in GURPS Powers™, p. 13, as a kind of movement, and p. 45, as a super-power, along with a new special enchancement, Attraction, and a new special limitation, Requires Low Gravity.
Page 55 also mentions:
- entities can “anchor” themselves to material objects as needed, allowing them to stand on floors, ride in vehicles, and so on. This is a standard feature of Insubstantiality
This appears to be a limited form of clinging to objects you can't even touch!
- Compared to Lizard Climb 
- Compared to Flight with Requires Surface 
- On Clinging by means of a line, like a spider