Book written by an American student's trite (5)
I believe the answer is:
banal
'trite' is the definition.
(I've seen this in another clue)
'book written by an american student's' is the wordplay.
'book' becomes 'b' (abbreviation for book).
'written by' says to put letters next to each other.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'student' becomes 'L' (learner, as in L-plates for learner drivers).
'b'+'an'+'a'+'l'='BANAL'
(Other definitions for banal that I've seen before include "boringly dull" , "Old hat" , "Everyday" , "Tediously unoriginal" , "Stock" .)