The Discreet is a confessor first, and an advisor second. The overt request for a Discreet in his official rôle is for the one who retains the Discreet to make a ritualistic confession: "My conscience stabs me". The Discreet then gives a ritual response: "I will bind the wounds".
The one who retains the Discreet will then provide the details of whatever troubles him, and the Discreet must listen without judging, and respond with the advice which will best soothe whatever those troubles may be.
Of all those with knowledge of the Arts of Discretion at the time of the disaster, only Pel is known to have survived.
At the time of Iorich, an Issola by the name of Lady Mifaant acts in a role that is at least very similar to that of the Imperial Discreet, although it seems she does not hold that title; according to the Teckla who mentions her, she holds no office, or at least none with a name, this is, of course, assuming that the Teckla is well-informed about such matters and not merely passing on Palace rumors.