Crump entered the College of William and Mary in 1835 and graduated three years later, having studied law under Professor N. Beverley Tucker.

A Democrat, he often delivered speeches on the subject of "States Rights" and supported John C. Calhoun for president in 1844, as well as the annexation of Texas.

The Virginia General Assembly in 1851 elected Crump Judge of the Circuit Court of Richmond to succeed John S. Caskie, who had resigned.

However, the new Virginia Constitution of 1851 changed the judicial system to permit popular election of judges the following year, and his position was terminated.

[10] After the war, upon the resignation of fellow lawyer Peachy R. Grattan as one of the City's representatives (part-time) in the Virginia House of Delegates, Crump succeeded to the position.

[12] He also was among the prominent speakers on April 29, 1870 at the memorial following the disastrous balcony collapse at the Virginia Supreme Court, and the following year helped gather funds for survivors of the Great Chicago Fire.