The DR3 (Danganronpa 3) anime airs in Japan at 11pm JST.

I've figured out when the anime airs in Eastern Standard Time.

Future Arc:
Airs Monday, July 11 at 9am EST. It continues every Monday at 9am until the arc is finished.

Despair Arc:
Airs Thursday, July 14 at 9:30am EST. It continues every Thursday at 9:30am until the arc is finished.

They will be streamed on Funimation and Hulu one day after.

I hoped this helped!