The phrase "second spouse" refers to a person's second husband or wife, meaning they are married again after their first marriage has ended, either through divorce or the death of their previous spouse. Full definition
Advised husband and wife who each had children from a prior marriage to ensure surviving spouse would be adequately cared for but children of first spouse to die would receive any remaining assets at second spouse's death (dkattorneys.com)
That means that you can reapply for ex-spouse benefits if you and your second spouse divorce, if your second spouse dies or if a court annuls your second marriage. (gobankingrates.com)