Son turns up at party with potato (4)
I believe the answer is:
spud
'potato' is the definition.
(spud can informally mean potato)
'son turns up at party' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'turns up' says the letters should be written backwards.
'at party' becomes 'dup' (I am not sure about this - if you are sure you should believe this answer much more).
'dup' in reverse letter order is 'pud'.
's'+'pud'='SPUD'
'with' acts as a link.
Can you help me to learn more?
(Other definitions for spud that I've seen before include "The popular potato" , "Commoner's King Edward?" , "Spade; potato (slang)" , "Potato (colloq.)" , "Tattie" .)