What is the name of movie based on shakespearan play in which real life husband and wife have enacted?

You're likely thinking of "The Taming of the Shrew" (1967) starring Richard Burton and Elizabeth Taylor.

They were a real-life married couple at the time and their off-screen relationship was famously tumultuous, which likely added some extra spice to their on-screen chemistry.

While there are other Shakespearean films with real-life couples, this one is the most iconic and readily comes to mind.