"Keep a rein on" is a phrase used to describe the action of controlling or limiting something. There are several alternative phrases that can be used to convey the same meaning, such as "keep in check," "keep under control," "restrain," "curb," "hold back," "keep a tight leash on," or "put a limit on." These synonyms can be used interchangeably depending on the context in which they are being used. By utilizing synonyms for "keep a rein on," one can convey the same message in a variety of ways, keeping the language fresh and avoiding repetition.