Given her previously expressed interest and the ambitious tone of her recent speeches, the senator’s attempt to convince the public that she is not interested in running for a second term is futile.
Can I replace the bold word by “Despite”?
No, “despite” would not make sense there. In “despite X, Y”, X needs to be something that makes Y seem less likely, not more likely. For example, you could say:
“Despite her continued denials, the senator’s attempt to convince the public that she is not interested in running for a second term is futile.”