The writer’s turned round story associated with university environment (6)
I believe the answer is:
milieu
'environment' is the definition.
(milieu is a kind of environment)
'the writer's turned round story associated with university' is the wordplay.
'the writer's' becomes 'im' ('writer's' could mean 'the crossword setter is').
'turned round' says the letters should be written backwards.
'story' becomes 'lie' (story can mean a fabrication).
'associated with' says to put letters next to each other.
'university' becomes 'u'.
'im' back-to-front is 'mi'.
'mi'+'lie'+'u'='MILIEU'
(Other definitions for milieu that I've seen before include "Environment - setting" , "'Surroundings, setting (6)'" , "Environmental condition, surrounding" , "(Social) setting" , "Social environment or set of surroundings" .)