Krdytkyu

The Drinker was begun in 1944 when Hans Fallada was imprisoned in a criminal asylum for the attempted murder of his wife. Author of two previous novels, his third, The Drinker, is autobiographical and tells the story, in diary form, of a man driven by the demons of morphine and alcohol.

https://www.theguardian.com/books/2007/sep/02/fiction.features1

Maybe I am a little bit slow on the uptake but I do not understand the passage in bold. The passage does not make sense to me. The subject "author of two previous novels" has no predicate. It seems to as if this part is cut off.

Your bolded text is not a clause but a noun phrase, which should be set in apposition to another noun phrase, its "predicand", which it describes. Usually the predicand is the noun phrase which immediately precedes the appositive:

Hans Fallada, author of two previous novels, started his third . . .

But when the appositive phrase falls at the start of a sentence it should describe the immediately following subject, like this:

Author of two previous novels, Hans Fallada started his third, The Drinker, in 1944 while he was imprisoned in a criminal asylum for the attempted murder of his wife.

The writer of this passage has carelessly disregarded this simple convention for establishing the predicand of an appositive, compelling the reader to figure out what it was the writer's job to make clear.

If we are willing to cut the author some slack:

Author of two previous novels, his third [novel], The Drinker, is autobiographical and tells the story ...

treating Author of two previous novels not as a noun phrase but as a kind of absolute construction.

You are almost correct. The intended meaning of the bolded fragment is that Hans Fallada had written two novels before he wrote The Drinker, and then the rest of the sentence describes the book. However, the way the sentence is written suggests that The Drinker (being Hans Fallada's third, though third what is unspecified) is the author of two previous novels. This is obviously nonsense, and therefore we have to search for other possible meanings.