Principal act, name I'm backing, American books (8)
I believe the answer is:
dominant
'principal' is the definition.
(I've seen this before)
'act name i'm backing american books' is the wordplay.
'act' becomes 'do' (to do is to act or execute a task).
'name' becomes 'n' (common abbreviation e.g. on forms).
'backing' shows that the letters should be reversed in order.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'books' becomes 'NT' (New Testament).
'n'+'im'='nim'
'nim' backwards is 'min'.
'do'+'min'+'a'+'nt'='DOMINANT'
(Other definitions for dominant that I've seen before include "Authoritative" , "Foremost, most important" , "Main, principal" , "Assertive" , "Exercising influence or control" .)