Since it seems that it is unlikely to be adding scheduled notifications to clients, maybe you should consider adding Zapier integration feature for new schedules.
i.e. New schedule for Job XYZ has been added
Zapier triggers auto email to client with an attached schedule for the week.
Hofsep Yousef commented
I think you are misunderstanding my point. The current integration sends an email out whenever there is ANY new schedule is added. You cannot select specific clients to receive their schedules.
i.e. we have multiple clients that we service their sites (which are jobs on Clockshar). We want them to receive their entire week schedule but their schedule only, not everyone else's. The current integration does not allow that.