If someone is described as a big fish in a small pond, they are very important or have a lot of influence but only in a small area or group.

Examples:

Paul is a manager of a small company; he likes to be a big fish in a small pond.

Jane might think she has power but she's just a big fish in a small pond.

Take note

If someone is described as a cold fish, it means that are unfriendly and don't show their emotions.

Example:

Julie's a cold fish; she never speaks to anyone in the office.