Does being a private investigator allow me to carry a concealed weapon?

No. Persons who carry or have access to a firearm while on duty must have a firearm endorsement as described under 6 VAC 20-171-365 of the state regulations. If carrying a concealed handgun, the person must also have a valid concealed handgun permit, and the written permission of his employer pursuant to 18.2-308 of the Code of Virginia.