Harry Brown is a great orator and . . . . . . . . politician.

'Harry Brown' is spoken about as an orator as well as a politician. Since both these aspects belong to the same person, article is also used only once to modify the noun, where 'a' modifies the phrase "great orator and politician". Hence article is not used before the noun 'politician'. If it's used, it changes the meaning of the sentence by saying that the politician is a different person.