Way to stop a youth’s initial lack of interest (6)
I believe the answer is:
apathy
'lack of interest' is the definition.
(I've seen this before)
'way to stop a youth's initial' is the wordplay.
'way' becomes 'path' (synonyms).
'to stop' means one lot of letters goes inside another (stopping can mean blocking a gap).
'initial' says to take the initial letters.
The initial letter of 'youths' is 'y'.
'a'+'y'='ay'
'path' put within 'ay' is 'APATHY'.
(Other definitions for apathy that I've seen before include "Absence of emotion or enthusiasm" , "Lack of emotion and enthusiasm" , "Complete lack of interest, indifference" , "Indifference - listlessness" , "Indifferent quality" .)