Wiktionary
kept man
n. A man who is supported financially by a female lover (usually a married woman).
Wikipedia
Kept man
A kept man is a man who is financially supported by a wealthy and often older person other than a spouse or close relative. Availability for some kind of social interaction is almost always expected in return. This can range from occasional to constant and from simple companionship to emotional and physical intimacy. A man may be kept by either a woman or another man. Being "kept" can be seen as a form of male prostitution if the relationship has a sexual dimension. The kept woman is a female version, more usually put under the umbrella term "mistress" and considered more common.