。
She'll probably write another book before long.
Literal
[topic-は] again soon book [object-を] will-write probably.
近く here is the adverb 'soon, in the near future' — different from the adjective form 近い ('close, near'). 近く paired with future tense gives 'soon (in the future)' or 'before long.' 本を書く ('write a book') uses the standard transitive 書く. The sentence implies the woman is a known author whose readers (or critics) anticipate her next work. The また ('again') flags this as the next in a series — common in commentary about prolific writers. でしょう adds polite speculation.