New Seasons of Zombies, Run! generally launch in mid-Spring (Northern Hemisphere). From the official launch date on we will release 2 new missions per week. We have a mid-Season hiatus which lasts around 1 month, and then begin releasing the second half of the Season on a 2 per week basis until the end of the Season. The final missions are generally released around the start of Autumn/Fall (Northern Hemisphere). Once a Season has finished you can still buy unlimited access to those missions with a Subscription.
If you can't see new missions on the week they are released, then try restarting your device or force-closing and re-opening Zombies, Run!