Antarctica has a thick ice cover and the highest average elevation of all the continents.

Does the combined new sentence use a compound subject, compound verb, or compound object?

The subject here is simple" it's just "Antarctica".

The verb is also not compound, it's a simple verb: "has".

The compound part of the sentence is the object: it is: "a thick ice cover and the highest average elevation of all the continents"

so the correct answer is "compound subject"