In most cases, there will be no difference at all. Latin doesn't have any words directly corresponding to the articles "the" and "a(n)", so "the new God" and "a new God" would usually both translate the same, novus Deus, which is word for word just "new God". In some rarer contexts where the idea of definiteness or undefiniteness is really important, something close to the idea of "the" can be expressed by a word meaning "that", for instance novus ille Deus = "that new God" (= the new God we know about or the well-known new God) and something close to "a(n)" can be conveyed by a word meaning "some/a certain", for example novus quidam Deus = "some new God", "a certain new God".