Born in Brunswick County, Virginia, Neblett received a Bachelor of Laws from Washington and Lee University School of Law in 1897.
He was a superintendent of schools for Grant County, New Mexico Territory from 1907 to 1911, and was a Judge of the Sixth Judicial District of New Mexico from 1912 to 1916.
[1] On January 29, 1917, Neblett was nominated by President Woodrow Wilson to a seat on the United States District Court for the District of New Mexico vacated by Judge William Hayes Pope.
Neblett was confirmed by the United States Senate on February 5, 1917, and received his commission the same day.
He assumed senior status on July 6, 1948, serving in that capacity until his death on May 7, 1950.