This is what is known as the “tube grip”, together with its retaining clip. This has been unavailable (obsolete) from Dyson for some time now.
We prefer to call a “tube grip” a wand collar. On Dyson DC15's, this little tube sits at the top of the wand and it is the bit you fit your tools onto. Click the photos above for a better look.
There are two types of DC15 wand - this is the one for the two-piece type with a half-circle retaining clip.
However, if you have the later type with a moulded red end, and you are practically inclined, this one can be fitted to later wands too. We have a tutorial on that >>here<<.
Available in light steel (originals were lavender or white) as you see above that will compliment any machine.
Please and be sure you are buying the right one - this is for a DC15 and that your machine is a DC15 and not a DC14 as they differ. The DC14 one is >>here<<.