A minor Instagram update released this morning lists only bug fixes in the description, but has quietly added a long overdue feature - a share sheet extension. With the new version of Instagram, it's possible to use the "share" feature in Photos or another app that supports share extensions to upload content directly to Instagram without needing to open the Instagram app.
When viewing images in Photos, selecting an image and then tapping on "share" now brings up Instagram alongside other sharing options like Facebook, Twitter, and Flickr. Selecting Instagram will allow users to write a caption before sending the image to Instagram.
As MacStories points out, Instagram's share extension is limited. Adding a caption to a photo is the only option, with no available photo adjustment tools or options for adding locations and people tags.
Instagram can be added to the share sheet through the Photos app by tapping on share, selecting the "More" button, and choosing to toggle on the Instagram option. Once that's done, Instagram will always be available in the share sheet of any app with share functionality.