I have a 4-5 year old kaffir lime in a container that was frozen this past winter. I resisted pitching the plant in hopes it might arise from the apparently dead. After several months of what appeared to be total dessication something resembling a root sucker appeared. I chopped down the rest of the plant to expose the sucker. Any suggestions about how to proceed with this plant? How do I extricate this sucker so it can exist in it's own pot?

I would leave it alone until it gets much bigger. It must still be being fed off the larger root system in the pot. If you seperate it you will have a small "seedling" again, I would let the old root system push it as much as possible to get some size back.

Was it a rooted cutting or a seedling? The sucker looks like kaffir lime but I'm asking on the safe side.
About helping the kaffir lime to survive - you can graft a small piece of the sucker to a rootstock, or try to root it. If the original plant died, you would have a grafted plant alive.

The original kaffir appears to be ungrafted. After five years, it still hadn't blossomed. The sucker is definitely a kaffir which I guess proves the original was not grafted?

If there were no flowers it must be a seedling or a rooted juvenile cutting.