"The child has hope."
Translation:Το παιδί έχει ελπίδα.
Um, yes. Adding the definite article in this case does not work unfortunately.
Only if you define within the same sentence what that hope is can you add it: The child has the hope to become a scientist - Το παιδί έχει την ελπίδα να γίνει επιστήμονας.
Saying the same thing and dropping the whole context after "ελπίδα" does not work.