In TNG: “The Defector”, Picard performs Henry V, and Data and he do the same in “Emergence”. Picard uses the excuse of the away team being actors performing A Midsummer Night’s Dream in “Time’s Arrow”. In DS9: “Improbable Cause”, Garak and Bashir debate Julius Caesar. In ENT: “In a Mirror, Darkly” the similarities between Shakespeare’s plays between the Prime and Mirror Universe are mentioned. Various bits of Shakespeare are quoted as well, notably General Chang, a Shakespeare aficionado in ST VI and Spock quoting Hamlet in DIS: “Perpetual Infinity”.
No love for Picard reciting a sonnet in TNG: "Ménage à Troi"? :) Or were you just specifically listing references to Shakespeare plays?
I always thought it would've been a fun twist if Harry got a promotion once Tom got demoted in Thirty Days.