。
My heart races with hope for the future.
Literal
Future [toward-への] hope [with-で] chest [subject-が] pounds.
胸が高鳴る ('one's chest pounds/throbs') is an idiom for excitement or anticipation — the heart beating faster. 未来への希望 ('hope directed toward the future') uses への as the directional modifier. A positive, uplifting sentence with a clean poetic structure.