Obnoxious son arrested by Labour leader over party (9)
I believe the answer is:
loathsome
'obnoxious' is the definition.
(thesaurus)
'son arrested by labour leader over party' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'arrested by' means one lot of letters goes inside another (inserted letters are held or arrested).
'labour leader over' becomes 'lo' (I can't explain this - if you can you should give a lot more credence to this answer).
'party' becomes 'at-home' (old-fashioned term for a party).
'lo'+'athome'='loathome'
's' inserted within 'loathome' is 'LOATHSOME'.
Can you help me to learn more?
(Other definitions for loathsome that I've seen before include "Disgusting, nauseating" , "Hateful" , "Detestable" , "Repulsive" , "15 [ABHORRENT]" .)