Vessbot is partially correct. At a major airport my experience is tower will issue a heading/alt to fly and ship you to the departure controller to sequence you back in. If at a smaller airport you might simply be told to turn downwind.
Below is the guidance in the ATC handbook.
7-4-1. VISUAL APPROACH
INTERPRETATION 24A visual approach is an ATC authorization for an aircraft on an IFR flight plan to proceed visually and clear of clouds to the airport of intended landing. A visual approach is not a standard instrument approach procedure and has no missed approach segment. An aircraft unable to complete a landing from a visual approach must be handled as any go-around and appropriate IFR separation must be provided until the aircraft lands or the pilot cancels their IFR flight plan.
- At airports with an operating control tower, aircraft executing a go-around may be instructed to enter the traffic pattern for landing and an altitude assignment is not required. The pilot is expected to climb to pattern altitude and is required to maintain terrain and obstruction clearance. ATC must maintain applicable separation from other aircraft.
- At airports without an operating control tower, aircraft executing a go-around are expected to complete a landing as soon as possible or contact ATC for further clearance. ATC must maintain separation from other IFR aircraft.