Send it to your carbon safety screen before your tailings hopper and recover it from there. If it is too fine for that then the probability of economic recovery and treatment is minimal.

Do you have an idea of how much gold is contained in carbon?

It would be good for you to get an idea of the average and the distribution, so that you can get an indication of what gross gains there are to be had. You will also need to assume an efficiency of extraction from the fine carbon.

Comparing these potential gross gains against the likely costs of winning the material will give you a good idea of the economic feasibility of your idea.

Try testing a sample in the lab using flotation with Diesel as the collector. This should produce a conc that can be filtered and incinerated. Will also let you know the economics of recovery.

The fine carbon can be recovered via a carbon safety screen (i.e. vibrating screen) before the tailings hopper. If it is too fine, then it can be economic recovery and treatment is minimal

There should be difference in specific gravity of fine carbon and loaded fine carbon. Can we apply any gravity separation technique to recover?

The difference between highly loaded and barren carbon might reach a few percent by SG, not enough to use. Carbon has about half the SG of typical rock. I have used a shaking table to remove rock from a carbon stream but at a coarse size. It is unlikely that a gravity device could do much unless it was fed a sized material. Screening the entire tailings at, say, 0.2 mm then processing the oversize would probably cost more than the recoverable values.

Can any chemical substance replace AuCN at the binding point?

I do not understand the question. It is unrelated to your post. Someone else suggested flotation recovery but that is not relevant to your question. Without experience I can only guess that flotation could be used, and guestimate that the cost is not worth the recovery or it would be used already. Gold in carbon carries significant costs at a refinery, do you have any numbers in these questions?

I'm gathering lots of ideas from here. After conducting attrition test on the carbon, I realised, the wear rate of the carbon is very minimal. Now, a cost benefit analysis is difficult because carbon regeneration procedure here is continuous making the determination of the total amount of fines generated from the kiln difficult to determine. Someone mentioned linear screening the fines recovery process. How helpful can that be?

I would like to ask if any chemical has more affinity to adsorb on activated carbon then it can replace NaAu(CN)2 at the binding point and thus forcing NaAu(CN)2 back to the solution which can be once again retreated with activated carbon and thereafter undergo elution.