There are some profiles on Instagram where you want to see the content they publish as soon as possible - it could be a news page or your favorite blogger. See how you can receive notifications for new posts, Stories, IGTV and Live.
You can turn on notifications for new activity and posts per Instagram account.

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

Here, search for select the profile you want to turn on notifications.

Here, tap the notification icon (bell) in the upper right corner.

You will see a menu to shows up in screen your. Select the toggles next to "Posts", "Stories" or "IGTV" to activate notifications for the corresponding post type.

If you want to enable notifications for all Instagram Live videos for the profile (By default, your Instagram notifies only for some video of Instagram Live.), Click the “Live Videos” button.

From here, select the “Recieve All Notifications”.

You can return and yes continue to use Instagram. Repeat this procedure for any Instagram account for which you want to enable notifications.
When there is new activity from this profile, you will look a notification for this on your smartphone.

This feature is available in specific countries, so you may not see the bell to activate notifications for each profile!
Source of information: howtogeek.com