Renouncing US citizenship may not have an effect on tax obligations. The US government still imposes taxes on US income for nonresidents. If you are renouncing your U.S. citizenship and are no longer planning to receive US income, you may be required to file taxes only for the portion of the year that you were still a US citizen.
Upon renouncing US citizenship, you may also owe an Exit Tax. Generally, if your net worth is under $2 million and you have not met the income test, you will not be required to pay an exit tax.