The phrase "tight rein" means to have strict control or supervision over someone or something, similar to how a person firmly holds the reins to control a horse. Full definition
First, rather than giving workers a true chance to prosper, the companies keep tight reins on key aspects of the business, restricting workers» earning potential while saddling them with hefty lease payments and reducing pay to poverty levels. (qz.com)
Canadian banks have also kept tight rein on developers. (nytimes.com)
First elected to the Council in 1999 ---- in a special election to fill Tom Duane's seat representing the West Village, Chelsea, and Hell's Kitchen after he was elected to the State Senate ---- Quinn has held tight reins over the Council's agenda as speaker while forging a working partnership with Mayor Michael Bloomberg. (gaycitynews.nyc)