Hi,

PCs may tie connections with some organisations/powerful NPCs that could, in return, provide some support : Guilds, Temples, Advisor of the prince, band of street kids...

i'd wish to houserule about this, maybe giving a specific card to the player, about what their contact may do, at which price.
Each card has a Influence stat, ranging from 0 (unknown) to, say, 5 (insider).
Each power has a difficulty rating, and player rolls influence vs difficulty just like skill checks (blue dice for influence, challenge for difficulty)

any idea ?

You can probably just handle this by using an Organization chart/card for each important organization that the PCs deal with, and adjust their influence with that organization on the org's track. The higher the PCs are, the more assistance the organization will provide. I wouldn't rely on a single die roll to determine whether or not the PCs get something from the organization.