An update of the setting of a play by Shakespeare to modern times could be found in

an adaptation

an imitation

a mockery

a tribute

An update of the setting of a play by Shakespeare to modern times could be found in an adaptation. Adaptations often take a book, film, stage play or television series and change it while maintaining its essence. For example, the 1999 movie Ten Things I Hate About You is an adaptation of The Taming of the Shrew, by William Shakespeare, set in a high school with teenagers as protagonists.