Something that's ascendant is increasing its power or status. An ascendant political party is one that captures more and more seats in Congress with every election.
Things are ascendant when they're growing in importance. It's common to use this adjective to describe people or groups that have already achieved a lot of power and whose influence continues to grow. Ascendant was originally a term in astronomy, although today it's used in astrology to mean the sign of the Zodiac rising in the east when someone's born. The Latin root is ascendere, "to go up," but also figuratively "to rise," or "to reach."