Progress seen in this writer's show (7)
I believe the answer is:
improve
'progress' is the definition.
(thesaurus)
'this writer's show' is the wordplay.
'this writer's' becomes 'im' (the person writing the crossword clues).
'show' becomes 'prove' (proving is a kind of showing).
'im'+'prove'='IMPROVE'
'seen in' is the link.
(Other definitions for improve that I've seen before include "Enhance" , "Get or make better" , "Ameliorate" , "Become better" , "Change for the better" .)