How do I replace old cane on a 3 piece setting?

You might be able to get pre woven cane at a craft store, if not available, ask if they would order some for you. There’s an extra part called a spline it will fit in the grove of the piece and and anker the cane.

https://www.youtube.com/watch?v=rDbkIZo6uBM

you would need to search the internet to order the items you need we have no way of knowing where to purchase the products in your area - good luck

LOok around for a craftsman who does cane, and see how much it would cost to have it done. It takes lots of practice to know how to do a good job.

https://www.amazon.com/slp/wicker-repair-supplies/79y6tjzt8cpr7b8

http://www.franksupply.com/wicker/furniture-repair.html

https://www.hardwareofthepast.com/antique-wicker-repair-supplies-s/1840.htm

https://homeguides.sfgate.com/wicker-furniture-repair-supplies-101099.html

I have a chair that also needs removed. I was quoted to repair was $2.00 per hole. Outrageous. I removed the caning and will replace it with another form of seating.

Your chair doesn't look like a normally attached cane seat. It almost looks woven into the sides, which would be very difficult to replace.

I agree with Deborah.. Here are some suggestions.

https://www.hgtv.com/design/decorating/design-101/how-to-fix-a-caned-chair-seat-

https://www.confessionsofaserialdiyer.com/simple-fix-for-a-broken-cane-seat/

You could look up some YouTube videos on weaving a cane seat to see if it gives you any ideas.

Thank you everyone for replying. I have started the internet search and have found some great info. Hopefully I can post something about what I have achieved.

ps...the cane needs to soak in water to be plyable