The huge 747 plunged through dense cloud cover on approach to Hamburg airport.
As far as we were taught, it should be:
The huge 747 plunged though dense cloud covering on the approach to Hamburg airport.
Is that right?
Both of these sentences are correct.
The huge 747 plunged through dense cloud cover on approach to Hamburg airport.
The "cloud cover" is used as a noun in this sentence. The use of such sentences is quite common among personals of Air Traffic Control Department.
The huge 747 plunged though dense cloud covering on the approach to Hamburg airport.
The "cover" is used as a verb and cloud is the subject of this verb.
Edit:
Colin Fine pointed out that your question was about the use of "the" in the sentence. "The" is an article that is used when talking about something specific. Using "the" in the first sentence would make the sentence more appropriate as the sentence is about a specific approach of a Boing 747. But as I wrote earlier, these sentences are common among the personals of ATC and they tend to keep their conversations short and specific, usually leaving out articles, as their primary concern is a safe landing and not the use of grammar.
Hope this helps.
Phrases like "on approach, upon departure, on arrival, at liftoff, in flight" do not use the definite article because they refer to a stage in a generic process. The definite article can be used, but would typically be used only if there was something unusual or particular, let's say the approach had to be diverted from its normal course.