Immunity against the variant you got is likely good for 1-3 years. New variants sometimes reduce the effectiveness of the neutralizing antibodies present because of changes to the protein structures. When that happens, immunity likely depends on the level of neutralizing antibodies in your system (low for people who got mild or asymptomatic cases, higher for more severe cases, and highest levels from the Pfizer and Moderna vaccines) and your level of exposure.
If you had a bad case and have high levels of neutralizing antibodies present, and you have a brief interaction with someone infected with the South Africa variant, you’re not likely to contract it even with some exposure. If you sit in a small room with a person infected with the South Africa variant and you had a mild case of COVID-19 with another variant, your risk is closer to that of someone who’s never had it before.
Normal rules still apply though. For example, if you’re outside, there’s almost no chance of transmission.