Bloodsucker's taken in current girl (6)
I believe the answer is:
louise
'girl' is the definition.
(girl's name)
'bloodsucker's taken in current' is the wordplay.
'bloodsucker' becomes 'louse' (blood-sucking parasite).
'taken in' means one lot of letters goes inside another (some letters have taken in others).
'current' becomes 'I' (symbol for electric current).
'louse' going around 'i' is 'LOUISE'.
(Other definitions for louise that I've seen before include "waitress in road movie" , "Sue, oil up the other girl" .)