The tannins which are released from most woods are harmless, and in fact are considered by some hobbyists to be good for the tank.
They will leech and turn your tank water into a "blackwater" tank. Basically, it'll look like weak tea. You have options!
1) take the wood out and boil it until the boiling water is almost completely clear. This forces the wood to leech more tannins more rapidly and thus keep your tank clear.
2) leave it in the tank and just do more PWCs until it clears. Some have had luck using purigen and/or activated carbon to pull a decent amount of tannins out.
Either way, Seachem Clarity won't really help since the color isn't due to particulates, per se. The product DOES work, but won't have any effect on the tannins.
🐟 Diana Lee 🐠
😎 the St. Augustine Redhead 😎