An auspistice is a "facilitator" or go-between of some sort between two others, mediating interactions between them and keeping their relationship functional. These are usually enemies (or something similar), also referred to as kismesis.
Auspistice is a portmanteau of "auspicious" (fortunate, promising) and "armistice" (truce.) It may be analogous to the ancient Greek concept of αγάπη (AGÁPĒ), or "selfless love," since the auspistice doesn't get anything out of this directly.
It is symbolized be a clover/club.
Eridan said that he and Vriska would likely become kismesis if Kanaya did not intervene and auspistice for them, which hints at the relationship between the two mediated parties being similar to, but distinct from, a kismesis relationship. Without auspistices, widespread black infidelity is guaranteed.