Currently, we have our job scheduling data stored in the database table. This allows the business user to alter the schedule in the database table through a customised screen. We are planning to migrate our scheduling framework to quartz. I have gone through the quartz documentation, it does not have anything to cover this requirement. Basically, if the schedule is changed, subsequent runs after the schedule job would be continued as per the new schedule, and this can happen without the restart.
You can reschedule the existing quartz trigger using this method http://www.quartz-scheduler.org/api/2.3.0/org/quartz/Scheduler.html#rescheduleJob-org.quartz.TriggerKey-org.quartz.Trigger-