Mr. Smith is one of the few actors in contemporary Hollywood who can largely control his own destiny by greenlighting projects on star power alone, and often coming on board as a producer.

He has several high-profile projects in development, most notably an Apple Inc. movie called “Emancipation” scheduled for release later this year that could put Mr. Smith back on the awards circuit in months.

Apple hasn’t made any changes to its plan for a late 2022 release, according to a person familiar with the matter.

The production of “Emancipation” reflects Mr. Smith’s signature star power. When he agreed to star in the film in 2020, the project became one of the buzziest titles at a virtual market held by the Cannes Film Festival. Mr. Smith stars in the true story of a runaway slave who escaped to the North and helped spark anti-slavery campaigns when photos of his lash-scarred back were published.