Boxer confused the fear with importance (13)
I believe the answer is:
featherweight
'boxer' is the definition.
(I know that featherweight is a type of professional boxer)
'confused the fear with importance' is the wordplay.
'confused' is an anagram indicator.
'with' says to put letters next to each other.
'importance' becomes 'weight' (weight is a kind of importance).
'the'+'fear'='thefear'
'thefear' with letters rearranged gives 'feather'.
'feather'+'weight'='FEATHERWEIGHT'
(Other definitions for featherweight that I've seen before include "Sportsman" , "Boxer; person not worth serious consideration" , "Boxing category" , "one might be counted out?" , "Nobody" .)