A playwright, or dramatist, was a person who wrote drama or dramatic literature. Their works could be performed, but could also be written literary works. One of the most famous Earth playwrights was 16th century William Shakespeare.
In 2368, Geordi La Forge attempted to sing "I Am the Very Model of a Modern Major-General" (from The Pirates of Penzance) by late 19th century playwrights Gilbert and Sullivan. However the USS Enterprise-D's collision with a quantum filament interrupted his performance. (TNG: "Disaster")
Lt. Commander Data had been preparing for a performance of HMS Pinafore (also by Gilbert and Sullivan) in 2375, before being assigned temporarily to a survey team studying the Ba'ku. (Star Trek: Insurrection)
In 2376, Lieutenant B'Elanna Torres crash landed on an L-Class planet and befriended the playwright and poet Kelis. In order to avert war, Torres aided Kelis to please a local warlord and created a play describing the adventures of USS Voyager. (VOY: "Muse")