A studor vent is an Air Admittance Vent/Valve, or AAV. Typically and ideally, plumbing fixtures have a vent pipe in the wall that goes all the way to the roof, and that pipe serves to allow air into the pipes to facilitate water flow...Just like holding your finger on a soda straw full of water, an unvented drain doesn't drain. When you remove your finger from the straw...Or vent the fixture...The water runs down.
In certain circumstances, plumbers can't run vent pipes for sinks, showers, and other fixtures. That's usually because the vent pipe is impractical, such as on a kitchen island. That's when an AAV is used. The AAV is installed downstream from the trap in the wall or in a cabinet. It has a one-way valve in it that allows the drain to pull air in through the AAV, but it won't let sewer gas escape.
Chances are, your old tub was vented. If the sink isn't draining, there's a chance that it was hooked up incorrectly or it isn't venting for some reason. You can certainly install an AAV between the sink's trap and the wall. The AAV needs to be above the drain level of the sink in most cases, glued to a vertical piece of PVC.