Penny, say, hugging American relative (6)
I believe the answer is:
cousin
'relative' is the definition.
(I've seen this before)
'penny say hugging american' is the wordplay.
'penny say' becomes 'coin' (penny is a kind of coin).
'hugging' indicates putting letters inside.
'american' becomes 'us'.
'coin' placed around 'us' is 'COUSIN'.
(Other definitions for cousin that I've seen before include "Son or daughter of an uncle or aunt" , "Aunt's/uncle's child" , "one in my family" , "An aunt's or uncle's child" , "person once removed?" .)