Final Fantasy IV
A 7 year old girl from Mist with a strong will and magical powers gets swallowed by Leviathan. She ends up being taken to the world of summoned beasts where time flows differently.
When the party reunites, she's already a young lady and can't use White Magic anymore.
You automatically aquire Shiva when Rydia rejoins your party. Rydia also grew to be a strong Black Mage and Summoner combined.
This version of Shiva has a lot more color and some simple animations. It actually looks closer to the FF8 or FF10 Shiva's design.
Shiva's only attack is Snow Storm, an Ice-Elemental attack on all enemies that can be done as many times as you want per battle.
It costs 30 MP to use and is a medium damage summon. It does most damage on Fire-Elemental enemies.
Callers were Shoukanshi (Summoners), and when you used Shiva, her attack was titled Fubuki (Snow Storm/Blizzard, same).