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.
If you have trouble threading light tippet through small hook eyes, magnifying Flip Focals make it much easier.
Some tenkara anglers fish without a net, but having one allows you to control and release the fish more quickly. 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.
If you have more than one fly, you will need a case to carry them. Still, you really don't need many flies, and the minimalist fly box
will hold all the flies you need for a day on the stream (or a week if you are careful with your back casts). It holds up to three dozen flies and can be worn on a lanyard or a zinger.
The Ebira rod quiver is a handy way to carry a rod, or a even a second rod, but for more protection you might want a light weight Rod Case.
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.
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.
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.
Tippet rings make tying your tippet to your line - and changing tippets when necessary - very easy.
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.
Fishing Gloves by Little Presents, the same company that makes the Wader Gaiters, provide warmth in winter and sun protection in summer.
Most tenkara anglers do not use "indicators," but some do. If you do, try the Nakazima Ball Floats, they're better than Thingamabobbers.