Smile broadly, having right to dip into drink (4)
I believe the answer is:
grin
'smile broadly' is the definition.
('grin' can be a synonym of 'smile broadly')
'right to dip into drink' is the wordplay.
'right' becomes 'r' (common abbreviation).
'to dip into' means one lot of letters goes inside another.
'drink' becomes 'gin' (gin is a kind of drink**).
'r' inserted into 'gin' is 'GRIN'.
'having' is the link.
(Other definitions for grin that I've seen before include "Cheeky smile" , "Look pleased" , "Smile while pulling back the lips" , "Smile wryly" , "Give a broad smile" .)