First, a caution: IFR procedures can (and do) vary between countries. It is incumbent on the pilot to study the respective authority's Aeronautical Information Publication (AIP) to understand local procedures before flight. When asking questions about instrument flight procedures, it is helpful to know which countries you are specifically traveling through. While the vast majority of countries simply adopt ICAO procedures, many have significant deviations (the United States included).
ICAO Doc 4444 (PANS/ATM) section 6.5.3 discusses instrument flight that terminates into a visual approach. Interestingly, the document is silent on what happens if the approach is aborted.
In the United States, the FAA is more explicit. In the Aeronautical Information Manual, section 5-4-23 addresses visual approaches. Paragraph (f) details what should happen if a visual approach is terminated:
A visual approach is not an IAP and therefore has no missed approach segment. If a go-around is necessary for any reason, aircraft operating at controlled airports will be issued an appropriate clearance or instruction by the tower to enter the traffic pattern for landing or proceed as otherwise instructed. In either case, the pilot is responsible to maintain terrain and obstruction avoidance until reaching an ATC assigned altitude if issued, and ATC will provide approved separation or visual separation from other IFR aircraft. At uncontrolled airports, aircraft are expected to remain clear of clouds and complete a landing as soon as possible. If a landing cannot be accomplished, the aircraft is expected to remain clear of clouds and contact ATC as soon as possible for further clearance. Separation from other IFR aircraft will be maintained under these circumstances.
(This aligns with the FAA's guidance for controllers, JO 7110.65 7–4–1, which says that ATC is not required to assign an altitude because the pilot is expected to climb to pattern altitude.)