Open the Instagram app on your iPhone or Android phone. Tap the profile tab, and on the profile tab tap the gear button. This will take you to Instagram’s settings. On the Settings screen, scroll down to the Notifications section, and tap on Push Notifications. You will find this screen is particularly long and with a customization option for every type of Instagram activity. Scroll down to the Live Videos section. Select the ‘Off’ option to turn off Instagram live notifications.
Once you’ve turned this option off, only the notifications that tell you an account you follow is live will be disabled. Every other notification that you’ve enabled will continue to arrive on your device.
While you’re at it, you can go through the rest of the options on this screen and disable every single Instagram alert that annoys you. These settings are device specific so if you use Instagram on more than one device, you will need to change your settings on each one.
There appears to be one shortcoming with this; you cannot selectively subscribe to Instagram live notifications for certain accounts. If you turn off story notifications, you still have the option to enable a story or post alert for select accounts. This same option isn’t available for Instagram live videos. You can try subscribing to post notifications for an account and maybe they will include a notification for when the account goes live but that’s highly unlikely.
One thing is worth appreciating here and that’s how much control Instagram gives its users over their notifications. You’d be hard pressed to find any app that gives as much control. Even if you’re an Android phone user with a rooted phone, you can’t get this level of control over your notifications from a single app.
This may help you,