The writer rotted away in the city (7)
I believe the answer is:
detroit
'the city' is the definition.
(Detroit is an example)
'the writer rotted away in' is the wordplay.
'the writer' becomes 'I' (the person who is writing these clues).
'away' is an anagram indicator (letters move away from their original places).
'in' is an insertion indicator.
'rotted' is an anagram of 'detrot'.
'i' going within 'detrot' is 'DETROIT'.
(Other definitions for detroit that I've seen before include "Motown, Mich." , "US city in Michigan" , "City in Michigan known for motor industry" , "U.S. city also known as Motown" , "Centre of the US motor industry" .)