Greek credit mainly applied to arts, oddly (5)
I believe the answer is:
attic
'greek' is the definition.
(from ancient Athens or Attica)
'credit mainly applied to arts oddly' is the wordplay.
'credit' becomes 'tick' (on tick can mean purchased on credit).
'mainly' means to remove the last letter (virtually or mainly the word, but not all of it).
'applied to' is a charade indicator (letters next to each other).
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
The alternating letters of 'arts' are 'at'.
'tick' with its final letter taken away is 'tic'.
'tic' after 'at' is 'ATTIC'.
(Other definitions for attic that I've seen before include "Lofty room" , "top-flight accommodation" , "Top storey" , "Classically elegant" , "28 [GREEK]" .)