There are some profiles on Instagram where you want to see the content they post as soon as possible – it could be a news page or your favorite blogger. Here's how to get notifications for new posts, Stories, IGTV and Live.
You can enable notifications for new activity and posts per Instagram account.

To get started, open the Instagram app on your iPhone or Android smartphone and tap the Search button from the bottom of the screen.

Here, search for and select the profile for which you want to enable notifications.

Here, tap the notifications icon (bell) located in the top right corner.

You will see a menu appear on screen . Select the toggles next to “Posts”, “Stories” or “IGTV” to enable notifications for the corresponding post type.

If you want to enable notifications for all Instagram Live videos for the profile (By default, Instagram only notifies you for certain Instagram Live videos .), tap the “Live Videos” button

From here, select “Recieve All Notifications”.

You can go back and continue using Instagram. Repeat this process for any Instagram accounts you want to enable notifications for.
When there is new activity from this profile, you will see a notification about it on your smartphone.

This feature is available in specific countries, so you may not see the bell to turn on notifications for each profile!
Information source: howtogeek.com
