Not entirely true, being overwhelmed by book award (2,4,6)

'not entirely' is the definition.
(to some degree but not completely)

'true being overwhelmed by book award' is the wordplay.
'true' becomes 'so' (similar in meaning).
'being overwhelmed by' means one lot of letters goes inside another (I've seen this in other clues).
'book' becomes 'tome' (a tome is a book).
'award' becomes 'degree' (degree is a kind of award).
'so' put within 'tome' is 'tosome'.
'tosome'+'degree'='TO SOME DEGREE'