If you pull out at the barrel more than 1.5mm, you really should use a gap-filling ring to maintain bore integrity. These are very easy to make these days. I have made most of mine from CDs or from the rings that come at the top of some CD spindles.
Tuning rings are put into the lower and larger end of the barrel, where you normally adjust for tuning. The point is that you don't want a gap in the bore like this:
| | lower end of barrel
The hole in a CD is just the right size (15mm) to fit virtually any clarinet. CDs can be cut with a sturdy pair of scissors.
Alan Segal sent this interesting comment:
Opperman was able to discern whether someone used a tuning ring or had merely pulled the barrel out without plugging the gap. I think Allard (your teacher) could do the same (these guys had great ears). Both recommended using the appropriate length of barrel if it was convenient to switch.