This article will teach you how to pin a chat on Instagram and discuss the limitations that come with doing so. Instructions apply to both Android and iOS versions of the Instagram app. You cannot pin a chat on the desktop version.
How to Pin Chats on Instagram | Pin Instagram DMs
You can pin a private or group chat in the Instagram app to the top of your posts, making it quick and easy to find. Here's how to pin chats in the Instagram app.
In the Instagram app, tap Messages in the top right corner.
Swipe left on the chat thread you want to pin to the top of your list.