Hi Natasha -
I would agree with Richi - if that 10K is not a target race, and you won’t be tempted to race it during the event, you could turn it into your long run. I think it takes more discipline to do that (not turn it into a race) than it does to just go out and do the long run on your own. But it could be a great teaching tool for learning how to hold back in the beginning of your Half marathon, while others take off too fast.
If you do want to race the 10K, you can add on some very easy warm up and cool down miles on either side of it, though maybe not a full 10K of them. Above all, listen to your body and don’t sacrifice your target run (the Half) for the 10K.
Certified Chi Running and Chi Walking Instructor