The key to adding cream to soup without the cream curdling is to temper the cream.
Before you add the cream to the hot soup you should get the cream hot slowly and temper the cream which is to bring the cream to the same temperature as the soup.
When the cream is heated and tempered to the same temperature as the soup then the cream should not curdle.
If you add cold cream or cool cream to hot soup then that is a cause of the curdling but having the cream the same temperature as the hot soup will prevent the cream from curdling.
Tempering, in its simplest form, means to bring two liquids you plan to blend together to a similar temperature before combining them completely.
Tempering is what keeps eggs from cooking when they’re added to a hot sauce and gives chocolate candy a perfect polish.
Learning to recognize when to temper in the kitchen will help you serve smooth sauces and soups.