Born in Williamsburg, Brooklyn, New York, Carew attended the public schools of Brooklyn and New York City and the College of the City of New York. He graduated from Columbia College in 1893 and from Columbia Law School in New York City in 1896. He was admitted to the bar in 1897 and thereafter practiced law in New York City. Carew was a member of the New York State Assembly (New York Co., 24th D.) in 1904. He was a delegate to the Democratic State Conventions held from 1912 to 1924, and a delegate to the 1912 and 1924 Democratic National Conventions.