Titaness's forlorn hope: to exist (6)
I believe the answer is:
phoebe
'titaness's' is the definition.
(Phoebe is an example)
'forlorn hope to exist' is the wordplay.
I cannot quite see how this works, but
an anagram of 'hope' is 'phoe' which is present in the answer.
'exist' could be 'be' (synonyms) and 'be' is found within the answer.
This accounts for all the letters.
This may be the basis of clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for phoebe that I've seen before include "flycatcher" , "who feeds on the wing and fly?" , "Apollo's sister Artemis, the moon goddess" , "Greek goddess of the moon" , "Greek goddess, daughter of Uranus" .)