Epoxy is about the only glue that will fill gaps. Whatever you use, don't use polyurethane glue such as Gorilla Glue. It will leave a mess and inhibit any subsequent repair.

bobismyuncle:

Thanks for replying. When using epoxy, can I stain over it?

I was thinking of mixing fine saw dust with glue (carpenter's glue) to fill, don't know if this will take satin either. Worst case, I might have to use paint to touch up.

You can mix wood dust into epoxy to get something that is somewhat stainable, however it will be quite different from the surrounding wood, requiring careful application of the right color stains with a fine artist's brush to recreate the color and grain across the break. This is typically a pretty high level professional refinisher's trick, so you may or may not want to try it at home.

One way or another you need to ad back structural material. Epoxy is one way, a carefully fitted piece of wood is another. Depending on your needs and the value of the piece it might be easier to have a carver make a new one for you. Museum restorations of such a piece might typically fill the gaps with an obviously non-matching material stabilize the structure but make it clear what is original and what is not.

Did you give a picture of your carving/ I would try wood filler that is sandable and stainable. You can build it up and carefully sand it down. Hopefully you can match the stain if there are any small pieces that have broken off test the stain on those. Sometimes in a small area if it is still too light you can use furniture pen to hide the mending spots.

But wood filler does not have the glue-ing property.

I am familiar with wood filler, have used it lately for other projects.