At a lively gathering, you'll often find a wet blanket sitting next to the life of the party.
Literal
Lively [attributive-な] seat [at-で], popular-person [possessive-の] next [to-に], fun-spoiler [possessive-の] person [subject-が] is-sitting [thing-こと] [subject-が] often exists.
A layered proverbial sentence. 陽気 here is a na-adjective 'cheerful / lively.' 人気者 ('popular person / center of attention') and 興ざめの者 ('fun-spoiler / wet blanket') are contrasted. ~ことがよくある ('often happens that X') is a general-truth frame. Delivers wisdom about social gatherings.