Youngsters qualify at the last minute (6)
I believe the answer is:
teensy
'minute' is the definition.
(I've seen this before)
'youngsters qualify at the last' is the wordplay.
'youngsters' becomes 'teens' (I've seen this in another clue).
'at the last' indicates one should take the final letters.
The final letter of 'qualify' is 'y'.
'teens'+'y'='TEENSY'
(Other definitions for teensy that I've seen before include "Mini" , "- - -weensy" , "Minute" , "Tiny" , "Very small" .)