No. Bhutan is generally relaxed and informal, and wearing formal attire such as suits or cocktail dresses would actually feel out of place, as locals and travelers alike dress simply and practically.
For everyday sightseeing, hotel dinners, and local restaurants, neat trousers with a sweater, fleece, or casual shirt are more than sufficient.
If you plan to attend a Tshechu (festival), smart casual clothing is recommended as a sign of respect, since locals will be wearing their finest traditional attire (Gho and Kira).

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