The fact that you are using a quill adapter tells me that you are keeping your existing threaded headset.

If you were going to a new all carbon threadless fork steerer then you would be doing a full “A-headset” threadless headset install.

In your case, the quill adapter has a wedge that locks down inside your steer tube by using a 6mm Allen wrench. There should be some allowable up and down movement to the threadless “quill”. Check the outer diameter of the quill adapter that fits the internal diameter of your steer tube and once you have this dimension, you could source some spacers to fill the gap between the bottom of the stem and the top nut of the threaded headset.

What diameter of ITM handlebars do you intend to go with - 31.8?