Learn Danish: Kunne du få udskiftet pakningen så den ikke drypper? - Could you get the gasket replaced so it doesn't drip?

This is the aspectual use of få combined with a past participle. It focuses on the achievement or completion of an action. It translates well to get replaced or manage to replace, emphasizing that the task of replacing the gasket is successfully finished, regardless of whether you do it yourself or have someone else do it.

Why does ikke come before the verb drypper at the end of the sentence?

The phrase så den ikke drypper is a subordinate clause (a dependent clause introduced by the conjunction så). In Danish subordinate clauses, central adverbs like ikke must always be placed before the conjugated verb, which is a key difference from main clauses where the adverb comes after the verb.

Could I just say få skiftet instead of få udskiftet?

Yes, in casual speech Danes often just say skiftet. However, udskiftet is more precise when talking about mechanics, repairs, or replacements. While skifte can mean a general change like changing clothes or changing your mind, udskifte specifically means to swap a physical component or part out for a new one.

Why is the pronoun den used for it here instead of det?