The correct option is D He ran so quickly that he soon overtook me.
An adverb clause is a subordinate clause which does the work of an adverb .It may, therefore, modify some verb, adjective, or sometime another adverb in the main clause.
In this case,
Option D is correct. He ran so quickly is the principal clause and that he overtook me is the subordinate clause. The subordinate clause modifies the adverb quickly in the principal clause like an adverb does. Therefore, it's a subordinate adverb clause.
Option A is incorrect because it's a simple sentence devoid of any subordinating conjunction.
Option B is incorrect because the two sentences have been joined by using an adjective clause because the subject 'he' in the principal clause is being qualified.
Option C is entirely irrelevant to the context because it doesn't retain the meaning of the given sentences.