The writer’s uplifting story, linked to high-class environment (6)
I believe the answer is:
milieu
'environment' is the definition.
(I know that milieu is a type of environment)
'the writer's uplifting story linked to high-class' is the wordplay.
'the writer's' becomes 'Im' ('I am' referring to the writer of the clue).
'uplifting' says the letters should be written backwards.
'story' becomes 'lie' (story can mean a fabrication).
'linked to' means one lot of letters go next to another.
'high class' becomes 'U' (as in U and non-U speech).
'im' backwards is 'mi'.
'mi'+'lie'+'u'='MILIEU'
(Other definitions for milieu that I've seen before include "(Social) setting" , "Environment - setting" , "'Surroundings, setting (6)'" , "Environmental condition, surrounding" , "Surroundings - location" .)