Horse-drawn carriages will be banned in New York City after the City Council approved a new bill Thursday that will end a Central Park tradition that’s endured for more than 150 years.

The City Council quietly passed a controversial bill that would give nonprofits the first shot at buying up distressed Big Apple properties. The “Community Opportunity for Purchase Act,” or COPA, requires some sellers to delay putting their properties on the open market for 90 days while “community land trusts” and other nonprofits have an exclusive...