Who does this? Scarlett Johansson, Natalie Portman
This is a shy, submissive individual who holds the glass protectively, not letting go, as though afraid somebody will take it away. Palms are kept hidden and the glass is used as a social crutch the drink is never quite finished, with a mouthful left in case of emergency.
The drink is small (maybe half a pint of lager for a man). It may be drunk through a straw, which is fidgeted with, and used to stir the drink between sips. The style and pace of drinking is an echo of those around them (very little is initiated).
This individual needs to be approached in a gentle, sensitive way, with perhaps a few understated compliments to build self-confidence, but may eventually warm to overtures.