gentlemanly; well-mannered; well-bred
Describes a man's behavior, attitude, or appearance as refined, courteous, and considerate, like a gentleman.
I was impressed by his gentlemanly manner.
I try to behave in a gentlemanly way.
礼儀正しい means 'polite' or 'well-mannered' in general, while 紳士的 specifically evokes the refined, courteous image of a gentleman.
From 紳士 (gentleman) + 的 (-like, -ly). The word 紳士 itself is composed of 紳 (sash, symbol of a gentleman) and 士 (samurai, gentleman).