The first is ungrammatical (the present perfect tense requires the past participle, "dried"; moreover, the phrase "has dries" cannot be used in English). The second is okay. However, the verb "to dry up" is typically not used like this.
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AnonymousAfter the varnish has fully dried upThis one. You have two verbs. "has dried". When the first of two verbs is "has", "have", or "had", the second of the two is always in its past participle form. ("dries" is a present form; the past participle is "dried".)