How to export video ready for Instagram

You can change the frame size of the project: press Command-J to open the project Inspector, then click Modify, and choose the desired size. I don't use instagram, but I suppose you'd want to choose "Square" 1080x1080.

You can do the above after duplicating the project, to keep the original version intact.

Or you can create a new project in the desired size, and copy and paste from one project to another.

Then you can use the new duplicate project function which will let you assign a new project and intelligently analyze your clips to reframe to fit the new format.

What OS and FCP version are you using?

As Tom said, this is a nice new addition in recent versions (maybe 10.4.9, I'm not sure), so you can use it to choose the new dimensions right there instead of the other options I had suggested.

The intelligent analysis only does so much, but it’s a good start. You’ll probably still have to play around with it a bit, especially if there’s motion on the camera.