Pay absolute attention to new author taking in English (4,3)
I believe the answer is:
hear out
'pay absolute attention to' is the definition.
(as in hearing out all that someone has to say)
'new author taking in english' is the wordplay.
'new' indicates an anagram.
'taking in' means one lot of letters goes inside another.
'english' becomes 'E' (abbreviation).
'author' anagrammed gives 'harout'.
'harout' placed around 'e' is 'HEAR OUT'.
(Other definitions for hear out that I've seen before include "Thoreau (anag)" , "Take everything in" , "Listen to everything" .)