From Longman Dictionary of Contemporary Englishrein something ↔ in (also rein something ↔ back British English) phrasal verb1 CONTROLto start to control a situation more strictly The government is reining in public expenditure.2 DSHto make a horse go more slowly by pulling on the reins → rein→ See Verb table
Examples from the Corpus
rein in• Bandelier did prompt his parents to take steps to rein Kip in.• Impressions gleaned in childhood and rein forced in adolescence cling like limpets into adulthood despite valiant efforts to shake them off.• I was used to riding with my reins hanging in festoons.• Hawkins was dozing on his seat, the reins loose in his hands.• I sat snug in the tooled leather saddle, the reins lying easily in one hand.• Just those in power want to keep their hands on the reins and in the tills.• Cadogan reins him in, you know.From Longman Business Dictionaryrein something → in (also rein something → back) phrasal verb [transitive] to start to control something more strictly and stop it from increasingThe government is reining in public expenditure.Surely the Treasury will want to rein back inflation? → rein→ See Verb table 