Vampire actor, he punctured child's skin and drew blood (7)

'drew blood' is the definition.
(leeches draw blood)

'vampire actor he punctured child's skin' is the wordplay.
'vampire actor' becomes 'Lee' (Christopher Lee played Dracula).
'punctured' is an insertion indicator.
'skin' means to remove the middle letters (only the skin or outside of the word is used).
'child' with its middle taken out is 'cd'.
'he' put within 'cd' is 'ched'.
'lee'+'ched'='LEECHED'

'and' acts as a link.