He graduated from the University of New Brunswick with a B.A. in 1886, then studied law for five years while working as the Fredericton correspondent for the Saint John Globe. He was called to the bar in 1892 and later founded the law firm of Phinney & Crocket in Fredericton, but he continued to work as a journalist part-time until 1904, the year he was elected to the House of Commons. He was a member of Parliament for nine years, resigning in 1913 to accept an appointment to the Court of King’s Bench Division of the Supreme Court of New Brunswick.
Three years later, he was also named Judge of the Court of Divorce and Matrimonial Causes of New Brunswick.
On September 21, 1932, he was appointed to the Supreme Court of Canada. He served on the Supreme Court for 11 years and retired on April 13, 1943. Justice Crocket died on March 2, 1945, at the age of 76. He is buried in the Forest Hill Cemetery in Fredericton.