Demi Moore is set for a recurring role on Fox’s hit hip-hop drama series Empire. Moore’s character will be introduced in the Season 3 finale this spring. She’ll play a take-charge nurse with a mysterious past who will become ever more treacherously entangled with the Lyon family in Season 4. Moore joins previously announced actors and musicians who will appear on Empire this spring, including her daughter Rumer Willis, Eva Longoria, Taye Diggs, Phylicia Rashad and Nia…