Be in the red, having zero points (3)
I believe the answer is:
owe
'be in the red' is the definition.
(I've seen this before)
'zero points' is the wordplay.
'zero' becomes 'o'.
'points' becomes 'we' (**).
'o'+'we'='OWE'
'having' acts as a link.
(Other definitions for owe that I've seen before include "Be in debt - woe is me" , "Be beholden" , "Have outstanding" , "overdrawn" , "Need to pay" .)