TMDb/No Way Out Celebrity Stream the classic thriller No Way Out on Prime. Kevin Costner stars as a naval officer trapped in a deadly political conspiracy of lies and murder. April 8, 2026 AceShowbiz - No Way Out is a classic 1980s thriller that combines sleek storytelling with a sharp political edge, a blend that has kept it popular decades after its release. Streaming on Prime until March 31, this tense drama starring Kevin Costner offers viewers a gripping narrative full of intrigue, deception, and suspense.