Indefinite article and preposition "as"

Why is it unnecessary to put an indefinite article before the word manager in the following sentence:

She took over as manager when Mr Hunt retired.

Why is it different from the case like this:

She is a manager.

Answer

Your first example contains what's known as a zero article and uses manager as a job title.

David Appleyard's Guide to Article Usage in English notes that:

An article is unnecessary in official job titles if there is only one person holding this position at any given time.
Example: George Osborne is (the) Chancellor of the Exchequer.

Although there may be multiple managers, of which Mr Hunt was one, the only manager position "she" could "take over" (given this limited context) was Mr Hunt's. This 'rule' is therefore applicable. If the sentence was "She became [a] manager when Mr Hunt retired.", that is, she became one of many managers but she was not necessarily filling Mr Hunt's vacated position, then the version with the indefinite article sounds better (and is consistent with the fourth of Appleyard's linked 'rules' under The Indefinite Article).

Your second example uses manager as a countable noun. The same guide notes that:

The indefinite article a or an is placed in front of a countable noun that is being mentioned for the very first time. Once introduced, all further references to it can be preceded by the definite article the.
Example: I have two cars: a Ford and an Audi. The Ford is white and the Audi is silver.