。
Where there's life, there's hope.
Literal
Life [possessive-の] exists [duration-間は] hope [subject-が] exists.
間は ('as long as / while') marks a duration. 命のある間 = 'the time during which life exists.' A direct calque of the English proverb — probably a translated aphorism rather than native Japanese phrasing, though Japanese has its own close equivalent.