If not immediately dispelled when cast, you may attempt to dispel a Remains in Play spell cast by your opponent during the Conjuration sub-phase of any of your subsequent turns. To do so, you may attempt either a Fated dispel or a Wizardly dispel (provided the Wizard making the attempt is within Dispel range of the Wizard that cast the spell).
Remains in Play spells do not retain the energy of their casting, and so you do not need to beat the original casting result if attempting to dispel in subsequent turns, but rather the minimum casting value given in the spell's description.