[1] It leaves the airfoil (which now has an equal but opposite "bound vortex" around it), and remains (nearly) stationary in the flow.
[2][3][4][5] It eventually decays through the action of viscosity, but before doing so it contributes significantly to wake turbulence.
The initial (and quite brief) presence of a starting vortex as an airfoil begins to move was predicted by early aerodynamicists, and eventually photographed.
Vortices either form continuous loops of constant strength, or they terminate at the boundary of the fluid - usually a solid surface such as the ground.)
The starting vortex is significant to an understanding of the Kutta condition and its role in the circulation around any airfoil generating lift.