I just received a civil warrant for court on a old credit card account. How do I solve this and not go to court?

First you need to consult a Tennessee attorney to determine if you have a defense of statute of limitations. If the debt is enforceable you probably can make a deal to settle if for 30 cents on the dollar.

If the statute of limitations had not run out on the debt, try to settle with the creditor.

Tennessee has a 6 year statute of limitations on consumer credit. However, that does not answer your question. You received a civil warrant, so you must go to court to fight the warrant if it is beyond the statute of limitations, or they will get a default judgment against you and follow it up with garnishment of your wages.