Originally Posted by glowe

The glue can also be hide glue, an old-time popular adhesive that was cheap and easy to use. Problem is that with both latex (rubber) or hide glue it that they are very weak. I do not think you need to worry about glue on the stock unless you find the other half. There are a few conservators out there that can replace the missing piece and if you want to keep them on the gun, I would seek out their advice. They will properly clean, repair, and give you a professional job. There is certainly a cost to this work, but it will be well worth the effort. I am the first to say I would be an amateur at repairing and conserving ivory and would definitely contact experts in the field.

Everyone has their own ideas on how to do stuff, unfortunately, some I have seen in this thread should not be attempted by amateurs. Here is some information I located that might help you out.

Cleaning
If the ivory object is in good stable condition, cleaning the surface of dirt and grime with a mild soap and water solution is appropriate. If the dusting is not enough the ivory can be cleaned with a mixture of water and mild soap (such as Ivory Snow or WA Paste). Never soak ivory as the water could cause the dirt to become more visible by embedding it into cracks or pores. Many liquids can be destructive to ivory so avoid if possible or contact a professional.

Stabilization and structural treatments
Avoid over the counter adhesives when repairing cracks or breaks of ivory. These repairs are difficult and the use of poor adhesives can result in staining of the ivory and embrittlement as the adhesives age. Breaks and cracks can be important historically and show its use of the object. Unnecessary repairs can result in the loss of that historical information. Contact a conservator before any structural repairs are made.

Surface treatments
Avoid wax or other protective coatings as they can age over time resulting in yellowing or darkening of the ivory surface. It can also obscure surface details that may be important to the object. The protective coatings can become difficult or even impossible to remove without damage to the object. If possible to remove unstable surface treatments, do so with appropriate solvents. Use caution and have a professional consulted before doing any work on the ivory.

Intervention
Especially in archaeological contexts, interventive treatment may in some cases be considered necessary. Such intervention is governed by conservation ethics, in particular the principles of reversibility and minimum intervention. Possible treatments include the reduction of salts to prevent further deterioration, and the consolidation of delaminating and friable components. Any treatment should be undertaken by a conservation professional.

Contact a professional
Ivory is extremely sensitive and reactive, if it is broken or extremely dirty please contact a professional conservator to conduct the repairs and extensive cleaning.

If you are going to pass this revolver down to future generations, repair and stabilization of those stocks is very important. One of the largest ivory restoration firms in the US is below and maybe a good place to call.

Ivory Repair, Ivory Restoration, fineart-restoration.com