Spousal support will not automatically terminate unless your court order specifically states that it will terminate upon the supported spouse cohabiting with a significant other. If your order does not include that specific language, you may still be able to terminate spousal support.
It is important to keep in mind that terminating spousal support under these circumstances creates a rebuttable presumption, not an automatic termination, that spousal support is no longer needed. If facts are presented to the Court that show that, despite cohabitating, your spouse still needs your financial support, the Court may deny the request to terminate spousal support.