Somewhere in one of my galleries there is an image of a 767 just before its wheels hit the tarmac. It's titled "The Moment Before The Decisive Moment".
Somehow this barn owl being frozen in mid air just before landing on the handler's glove seems almost cooler.
For any other visitors with the same question as Mairéad, I'm afraid I can only offer a best guess. Looking at the full size image it's clear that this isn't something that the owl is clutching; the talons are fully extended. I believe that it's attached to the left hand ankle band.
It's also not a stick. In some of the later shots that I took at this time I could see the keeper take hold of it and curve it over his glove. It therefore appears to be semi-rigid but bendable, rather like an old fashioned pipe cleaner.
Web searches didn't help a great deal but I did come across a device used in falconry called a "jess". Commonly made of leather, it's used both to help the bird balance while sitting on the glove, and can also be used to secure the bird to a perch outside of the aviary. While this doesn't look exactly like the jesses that I've come across, I think that it may be for the same purpose.