Tenkara accessories are all those things (beyond your rod, line and fly)
that it turns out you really do need.
And since you will need more than a rod, line and fly, you will need something to carry it in. The ZimmerBuilt Tenkara Gear is specifically designed for tenkara anglers.
I am often asked, "What do I need to start tenkara fishing?" Besides the rod and the line, you will need a way to manage the line when the rod is collapsed. I would recommend either the Tenkara Line Holders or the Fuji EZ Keepers. The EZ Keepers are a little more convenient, but the Tenkara Line Holders allow you to store the line when it is off the rod, and you can store it with the tippet and fly still attached. I recommend getting two so you can have lines of different lengths.
Streamside tools (hemostats, nippers, a zinger) will be necessary if you don't already have them.
Some tenkara anglers fish without a net, but having one allows you to control and release the fish more quickly. The Daiwa Keiryu Damo has a knot-free, fish-friendly bag. If you have a net or a wading staff, and I would recommend fishing with both, you will want something to tether them so you can drop them when unhooking a fish or taking a photo and not have them float away. I really like the Gear Keeper for that. It's like a zinger on steroids.
The Shimano Net Leash has a novel attachment system that works better with Japanese tenkara and keiryu nets (and the Titanium Net) than American leashes do.
Although tenkara fishing requires little in the way of gear, you may want something to carry a lunch, a water bottle, and maybe a light rain jacket. If you also need to carry a pair of rolled up hippers, and a few more odds and ends, the Fishing Backpack would be the perfect size.
More and more tenkara anglers are replacing their heavy, bulky fishing vests with a minimalist chest pack (or over the shoulder, hip pack) like the Tippet/Fly Pouch.
If you have more than one fly, you will need a case to carry them. The EasyGrip™ Foam
Fly Box holds flies securely without damaging the foam. It fits in your pocket or the Tippet/Fly Pouch. The Magnetic Midge Box holds all those flies that are too tiny to slide into foam slits or dig out of compartments. For the true minimalist, the minimalist fly box holds up to three dozen flies and can be worn on a lanyard or a zinger.
Tippet rings make tying your tippet to your line - and changing tippets when necessary - very easy.
And after you've netted the fish? In some circles, catch and release has become little short of a religion. I am not a religious person. If you are backpacking and hoping for a fish dinner to supplement your freeze dried food (or if you just happen to enjoy a fresh fish dinner from time to time), you will need a way to carry your catch. You could do a lot worse than the Tenkara creel.
The Fuji Rod Caps are nice as a backup tip cap or as a replacement for the cap that came with you rod. They hold securely and are large enough that they are hard to lose. Replacement lillian is also a backup that you'll hopefully never need, but it is better to have it and not need it than need it and not have it.
The C&F 2-in-1 Retractor is good for keeping tools like Angled Nippers or a Figure 8 Tool handy but out of the way.
You might want to consider a pair of the wader gaiters that Dr. Ishgaki wears. They protect your expensive waders (and your knees) when kneeling to keep a low profile. Stealth really is the key to fishing a short line and kneeling where possible is a very good way to be stealthy.
Most tenkara anglers do not use "indicators," but some do. If you do, try the Nakazima Ball Floats, they're better than Thingamabobbers.
The Daiwa Figure 8 Tool makes tying figure 8 knots, surgeons loops or perfection loops - any knot where you have to reach through a loop to grab the line - very easy.
Most of the people coming to tenkara are already fly fishermen, so most will already have waders and wading boots. Whether you are new to fly fishing or just new to tenkara, for fishing the small streams where tenkara really shines, consider a pair of hip waders.
Personally, I do not even step into the water without a wading staff. The most convenient may be a folding staff like the Folstaf wading staff or Simms wading staff, but you can also make your own from a broomstick or shovel handle purchased for just a few dollars at a hardware or home improvement store.