This discovery will give new hope to HIV/AIDS sufferers.
a feeling that something good will probably happen
thinking that this would happen (It may or may not have happened.)
stopped believing that this good thing would happen
wanting something to happen (and thinking it quite possible)
showing concern that what you say should not offend or disturb the other person: a way of being polite
wishing for something to happen, although this is very unlikely
Explanation
Option A is correct because in the sentence 'This discovery will give new hope to HIV/AIDS sufferers,' the word 'hope' refers to the expectation or feeling that a positive outcome (like a cure or better treatment) will likely happen in the future as a result of the discovery. It does not imply a mere wish against odds (which would be option F), a past assumption (option B), or politeness (option E).