Originally described wealthy individuals not needing to work, often in British aristocracy. In historical novels, characters are often portrayed as gentlemen of leisure.
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Modern Nuance
Today, it may imply someone who is well-off but it's also used humorously for anyone relaxing. On vacation, I'm just a gentleman of leisure, no emails or calls.
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Cultural Perception
Some may view a 'gentleman of leisure' negatively as lazy or unproductive. My neighbor calls himself a gentleman of leisure, but others see him as idle.