This key art for Star Trek III: The Search for Spock is by Gerard Huerta (artist
signature on the lower right side of the art). This art was used for STIII’s theatrical poster campaign in the US, examples of which can be viewed here.
Huerta is predominantly known for his letterform and logo design; this is one of the few movie posters he created or co-created. While most sources credit this art to Huerta alone, some sources list Huerta and Roger Huyssen as co-artists. Based on the work Huyssen did for the "Vengeance of Khan" title, I speculate that Huyssen did the title lettering for the final version of this poster (and possibly the starry elements), seen below, while Huerta was responsible for the face of Spock.
Note that the final design elements of the Enterprise and the Klingon Bird-of-Prey are absent from the original illustration. They are photographic elements—likely added during the graphic design and layout phase along with the film title, poster border, credits block and corporate logos—and are not part of Huerta's original artwork.
In
discussing this artwork, we must also recognize Spiros Angelikas,
designer and owner of the Spiros Associates design firm, for his art
direction. Art like this for a major studio production is typically a
collaborative process, and Angelikas worked alongside Bob Peak on the
poster art and design for the first several Star Trek films and many
others. For further reading on Mr. Angelikas, check out this post at TrekCore.
