Magazine has a few words on severe punishment (4,8)
I believe the answer is:
life sentence
'severe punishment' is the definition.
'magazine has a few words' is the wordplay.
'magazine' becomes 'life' (former US magazine).
'has' is a charade indicator (letters next to each other).
'a few words' becomes 'sentence' (I've seen this before).
'life'+'sentence'='LIFE SENTENCE'
'on' is the link.
(Other definitions for life sentence that I've seen before include "Judges may confirm such" , "short extract from American magazine" , "Long prison stay" , "Long-term punishment" , "Very large bird" .)