Making Mark proud of himself, impressing duke with drink (8)

'making mark' is the definition.

'proud of himself impressing duke with drink' is the wordplay.
'proud of himself' becomes 'smug'.
'impressing' means one lot of letters goes inside another (impress historically meant to conscript).
'duke' becomes 'd'.
'with' is a charade indicator (letters next to each other).
'drink' becomes 'gin' (gin is a kind of drink**).
'd'+'gin'='dgin'
'smug' enclosing 'dgin' is 'SMUDGING'.