Queen is as nothing I suspect, after jack’s special quality (2,2,4,4)
I believe the answer is:
je ne sais quoi
'special quality' is the definition.
(special quality which cannot be described)
'queen is as nothing i suspect after jack's' is the wordplay.
'nothing' becomes 'O' (looks like zero - 0).
'suspect' is an anagram indicator (a suspicious or unusual spelling).
'after' says to put letters next to each other.
'jack' becomes 'J' (playing card abbreviation).
'queen'+'is'+'as'+'o'+'i'='queenisasoi'
'queenisasoi' is an anagram of 'enesaisquoi'.
'enesaisquoi' put after 'j' is 'JE NE SAIS QUOI'.
(Other definitions for je ne sais quoi that I've seen before include "Special unknown ingredient" , "Quality that can't be easily described" , "(A certain) something" , "Elusive but pleasing quality" , "Indefinable quality" .)