If you incur a new debt after you file for bankruptcy, it can never be discharged in that proceeding. You can't go back and add it. Bankruptcy can only address money you owe at the time you file your petition. You're responsible for paying anything that comes along after this.
When you file for Chapter 7, the trustee seizes your assets and liquidates them to pay off your debts, but the bankruptcy law allows for exemptions, which you can use to protect certain assets from seizure and sale. When a debtor has no property that the trustee can sell, the case is said to be a no-asset bankruptcy. At least two bankruptcy courts have specifically ruled that if you filed for Chapter 7 protection and if yours was a no-asset case, debts you owed at the time of your bankruptcy are included in your discharge even if they were not listed in your petition. This is because none of your creditors received any payments, so the one you forgot wasn't unfairly prejudiced even though you forgot to include it -- the debt would not have been paid anyway.
If the trustee liquidated any of your property, yours was not a no-asset case. In this case, you still owe any debts you forgot to include in your petition. If you had remembered to include the debt at the time you filed, the creditor would have received some of what you owed when your property was liquidated, so you must either re-open your bankruptcy case to discharge this debt or you're responsible for paying it.
Amending the Petition
To add a forgotten creditor to your bankruptcy after discharge file a motion with the court to re-open your case and amend your petition. This is not as simple as it sounds. Several complicated issues are involved, such as how the forgotten creditor can or should receive payment toward the debt if all your non-exempt assets have been liquidated and the money already distributed. You'll have to pay additional filing fees and probably need the help of an attorney. Even if yours was a no-asset bankruptcy, the forgotten creditor might insist that you reopen the case to include its debt, but courts have ruled that you're either not allowed to do this or don't have to do so if none of your creditors received any payment as part of the proceedings. An attorney can explain this to them.
If you filed for Chapter 13 bankruptcy, rather than Chapter 7, the issue is much more clear cut. If you omitted a creditor, the debt is not discharged. Chapter 13 involves funding a repayment plan to your creditors with your disposable income each month over a period of three or five years. Therefore, if you had included the debt in the first place, the creditor would have received some payment from the start. Discharging the debt after you completed your plan would unfairly affect the creditor.