Good carbon is usually very adsorbant, which means as soon as it is exposed to water, its adsorbing sites will be become saturated very quickly. Really, 24 hours is enough for the carbon to be saturated.
So, if you use it to clear up tannins, a job which carbon will do ImperfectFaerie, it will have to knock the other adsorbed chemicals off the sites. Which is just technical jargon for, to adsorb something else, the firs thing that was on the carbon will have to come back off.
Once you've exposed it to water, you should probably consider that carbon used up.
Now, exactly why are you wanting to get rid of the tannins? The color may be unappealing, though for many fish it is much more like their natural waters, it may even be a spawning trigger for some species. Not only that, but tannins perform some other really great duties in an aquarium; most importantly for the fish, tannins detoxify heavy metals by binding the metals up. Heavy metal poisoning is often overlooked as the concentrations of some metals in tap water that is safe for humans, can be very unsafe for fish. Copper is a great example, by the time the average person can taste copper in their water, it is still at a safe level for humans, but is over 1000 times the toxic threshold for the average fish.
Not only do tannins bind up the heavy metals, but in that bound up state, plants can uptake the heavy metals much more easily. In this way, the plants have a much lesser chance of lacking their micronutrients. So, if you have live plants in your tank, the tannins help them too.
Though, if you insist on removing the tannins, water changes and some fresh carbon will do it. Though I would consider just keeping it exactly the way it is now for all the benefits I outlined above.
