Son ends up going off to stay for a while (7)
I believe the answer is:
suspend
'stay for a while' is the definition.
(stay can mean to suspend or postpone)
'son ends up going off' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'going off' is an anagram indicator (letters go or move around).
'ends'+'up'='endsup'
'endsup' is an anagram of 'uspend'.
's'+'uspend'='SUSPEND'
'to' acts as a link.
(Other definitions for suspend that I've seen before include "Put in abeyance" , "Bring to a temporary halt" , "Ban" , "Dangle or postpone" , "Hang freely" .)