The phrase "closed circle" typically implies a group that is exclusive or difficult to penetrate. There are several synonyms for this phrase that convey similar meanings. "Inner circle" suggests a group that is more influential or important than others and often involves a sense of secrecy. "Clique" implies a group that often excludes others and may be viewed as unfriendly or elitist. "Cabala" suggests a secret system or organization that may involve hidden knowledge or beliefs. "Elite" suggests a group that is superior in status or ability, while "exclusive group" simply implies a group that is difficult to join. Ultimately, the choice of synonym depends on the context and the intended tone or emphasis.