Fruit gives family zero scope (5,6)
I believe the answer is:
blood orange
'fruit' is the definition.
(I've seen this before)
'family zero scope' is the wordplay.
'family' becomes 'blood' (blood can mean one's family).
'zero' becomes 'O' (O resembles 0).
'scope' becomes 'range' (synonyms).
'blood'+'o'+'range'='BLOOD ORANGE'
'gives' acts as a link.
(Other definitions for blood orange that I've seen before include "Fruit" , "Citrus variety" .)