The Inheritors are not a guild as such. Guilds are upstart new fangled things with which they perhaps condescend to engage when it is convenient to them. They represent true class and stability, the kind that cannot be gained through merely working one's way up. Some people are just born to lead.
The loose social grouping that is the Inheritors consists near entirely of those who were born within the city to the rich, established and powerful. The only life they have known (usually) is the rarified one available only to the pinacle of city society, amidst the movers and shakers both guild affiliated and otherwise. The connections and resources inherited from their forebears stand them in good stead in this world, and many of them maintain the success that their parents/forebears/brood mothers have achieved.
Some deign to affiliate themselves with other guilds, when it suits them, as there is a begrudging acceptance that this tends to be the quickest route to power these days. However, over and above loyalties to other guilds there tends to be a special sort of society between those who count themselves among the Inheritors. Family ties, loyalties and bitter rivalries tend to keep them well in touch. This network tends to aid them in procuring services within the city for very reasonable prices, or favours promised.