Map depicting the Kazon sphere of influence
A sphere of influence was a metaphorical area surrounding an organization, location, or person where they had a certain amount of power to influence the decisions and thinking of others.
In 2268, Arne Darvin noted that according to the Spacematic's ship's log, Cyrano Jones was within the Klingon Empire's sphere of influence less than four months prior to his visit to Deep Space Station K-7. This fact made him a viable suspected Klingon spy, something Nilz Baris agreed was possible. (TOS: "The Trouble with Tribbles")