Posted 17 May 2017 - 02:21 AM
Which version of iOS are you running?
In iOS 10, you can have overall "Allow Notifications" turned on, but have "Upcoming Events" turned off (this is how my iPhone is set as I use a different calendar app than the built-in one, so I don't want the build-in Calendar app "chirping" at me). If forget how iOS 9 handles it.
Next, I just want to make sure you and I are on the same page as to what you are after. Do you want the little red circle with a number that shows up on the Calendar app icon (that is a "badge")? Or do you want an "alert" (with or without sound) that pops up on the screen? "Alerts" can take the form of what Apples calls alerts or banners (at least in iOS 10...it is similar for iOS 9, but I don't recall if they are named the same or operate the same). For "badges", you need to make sure that in the Notifications settings for Calendar, that the "Badge App Icon" switch is set to on. If you want an "alert", then you have to set with the "Alert Style When Unlocked" to either "Banners" or "Alerts". If you want that "alert" to show up on the lock screen (i.e. when the device is locked), then the "Show on Lock Screen" switch needs to be set to "on". And last, if you want a sound for an "alert", then make sure the "Sounds" item in the Notifications settings for Calendar is set to something other than "None".
Next, have you set an "alert" with in the appointment/event item within the Calendar app? If you want an alert to popup and potentially make a sound, then you need the alert option set in the appointment/event. If forget if this is also true of "badges" or not. If you just create an event/appointment that does not alert option (typically something like "2 hours before" or "at start"), then it will not do any sort of popup alert (with or without sound) on either the lock screen or when unlocked.
Last, with iOS 10, there is an "Up Next" widget on the Widgets/Today View screen that you can have activated. If you do, then it will list the next upcoming event(s) in that widget. You can then move that "Up Next" widget to the top of the list of Widgets if you want to see it first. If you are not familiar with the Widget/Today View screen, you get to it by swiping left from the lock screen when the phone is locked (assuming you have it set to allow access to the Today View screen when the device is locked) or swiping left from the 1st/left most home screen. iOS 9 had a similar "Up Next" widget, but iOS 9 had widgets in the same place as the Notifications list...i.e. you swipe down from the top to get to them. For the "Up Next" widget, it does not matter whether you have an alert set in the event nor does it matter what you have setup in terms of the Notification settings for the Calendar app...the next event will always appear there.