Son eager for heavy drinking (8)
I believe the answer is:
swilling
'heavy drinking' is the definition.
(swill can mean to drink large quantities)
'son eager' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'eager' becomes 'willing' (similar in meaning).
's'+'willing'='SWILLING'
'for' is the link.
(Other definitions for swilling that I've seen before include "Drinking greedily" , "drinking large amount" .)