In the situation you described, you are entitled to claim the dependent and not the noncustodial parent. The tax law and applicable IRS rules take precedence over the language in a divorce decree, where there is a conflict. If parents are divorced and do not live together, the custodial parent may sign a release which allows the noncustodial parent to claim the child as a dependent and claim the child tax credit/credit for other dependents for the child, and dependency exemption, if the requirements are met.
The custodial parent must use either Form 8332 or a similar statement (containing the same information required by the form) to make the written declaration to release a claim to an exemption for a child to the noncustodial parent. Although the exemption amount is zero for tax year 2024, this release allows the noncustodial parent to claim the child tax credit, credit for other dependents, or additional child tax credit, if applicable, for the child. The noncustodial parent must attach a copy of the form or statement to their tax return.
@xmasbaby0 is correct that because the dependent is over 17, they can only qualify you for the Credit for Other Dependents. Since the dependent is a full-time student under age 24, the gross income limit doesn't apply.
See this TurboTax tips article and IRS Publication 501 for more information.
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