'considerable fame' is a correct and usable phrase in written English.
You can use it to describe a situation wherein someone or something has become widely known or celebrated, such as in the following example sentence: After her novel achieved considerable fame, the author was invited to speak at a number of literary events.
During her lifetime Olsen gained considerable fame, particularly among scholars.
Lawrence had found considerable fame – though not fortune – quickly.
Kemp himself was beginning a period that would bring him considerable fame, if not riches.
When his owner chopped off his head, Mike continued to live and then acquired considerable fame on the carnival circuit.
His book: "Ways of the Hand: The Organization of Improvised Conduct" brought him considerable fame both within and outside the world of academe.
Speaking of Davies, it is worth reflecting that she owed her considerable fame, at least initially, to a silver medal in the 1980 Olympics.
His uncle, Israel "Cachao" Lopez, was an even more celebrated bass player who enjoyed considerable US fame after choosing exile in Miami.
The family included Ludwig Wittgenstein, one of the 20th century's foremost philosophers, and his brother Paul, a musician who after losing an arm in World War I went on to gain considerable international fame as a one-handed concert pianist.
Raoul Wallenberg surely deserves his considerable posthumous fame, and Bernadotte should be restored to his rightful place in history alongside his countryman.
She gained considerable YouTube fame when she posted a video of herself singing "Total Eclipse of the Heart" in the voices of 19 different divas in 2013.
It's highly likely, many commentators have noted, that Keegan would have achieved considerable literary fame and success had she lived.
