Here are a few updates, and will add more as races make decisions about how to support safe events. In the meantime, you can find plenty of virtual races at RunSignUp, Running in the USA, etc.

April 23-25 Socks & Undie 5K Raleigh
April 24 MAD Dash 5K Dobson
April 24 Owls Roost Rumble Greensboro
April 24 NC Spring Classic Holly Springs
May 1 Triangle Race for the Cure Anywhere
May 1 Triad GO FAR Community 5K High Poing
May 1 Run for FUNds Lillington
May 1 Smile More Complain Less 5K New Hill
May 1 Feet for the Street 5K Winston Salem
May 8 Medoc Spring Race Hollister
May 8-23 Philosopher's Way Trail Runs Chapel Hill
May 9 Mother's Day 5K Raleigh
June 5 Running of the Bulls 8K Durham
June 20 Father's Day 5K Raleigh
June 26 Ultimate Runner Winston Salem
July 17 Flip Flop 1K Cary
Sept 18 Run the Quay Fuquay-Varina
Sept 18 St. Paddy's 4 Miler Raleigh
Oct 9 Oktoberfest 4 Miler Raleigh
Nov 13 Shakori 40 Pittsboro