Is is correct to write: 'Author Martin Amis describes...', or should we use the article 'the' in front of 'author'?
"The" is not required.
There are many examples where a profession is prefixed to a name. For example:
However, I'm quite sure that it is context dependent. For example, let us say we are talking about your author describing a door.
is slightly different to
So pick whichever one you need.
Both are possible, but I think the difference is one of formality. Author Martin Amis might be found in a popular newspaper, but a piece of academic prose would be more likely to refer to the author Martin Amis, assuming it wasn’t enough simply to write his name alone.
It's actually a property of a word whether it can be used this way or not. Compare:
Author can be anarthrous and sheep can't. Just about every profession a person can hold is ok to use without "the" and as for all the other nouns in English, I don't think there's really a rule. Off the top of my head, all the examples I can find are nouns describing something a person is. I mean that nouns like table, blizzard, whisper, and so on can't be used like this, while schoolboy, housewife, candidate, and so on all can. But I'm not sure that's a rule, it might just be that my imaginary sentence generator is slow this morning.
Not sure why that's ok and Sheep Dolly isn't.