Galadriel and Gandalf are both ancient creatures in The Lord of the Rings. Even though the grey wizard seems to hold the Lady of Galadhrim in reverence, the history of Arda reveals that it is she who should be diffident towards the Istari, and not vice versa.
For one thing, Gandalf—or Olorin as he was known in the beginning—is one of the Maiar, lesser angels who served Ainur, their greaters, and helped them shape Middle-earth as we know it. Galadriel is a Noldorin elf of high standing, akin to Feanor in a lot of ways, but she will nonetheless find it difficult to go toe-to-toe with one of the Maiar, despite wearing one of the elven rings of power as she does in the Third Age.
Raw strength and race aside, do we know which character is older than the other?
Who is older, Gandalf or Galadriel?
According to The History of Middle-earth, the Maia who came to be known as Gandalf in the Third Age was created by Eru himself at the moment of creation before the Music of the Ainur. As for Galadriel, the daughter of Finarfin was born in Valinor during the Years of the Trees, 1362 YT, to be precise.
That means that even though both characters are thousands of years old when The Lord of the Rings takes place, Gandalf is still some 5,000 years older than Galadriel. After all, he was around during the 3,500 Years of the Valar, and adding that to the 1362 Years of the Trees brings the tally close to that number, give or take.
Believe it or not, during The Fellowship of the Ring, Gandalf is approximately 12,000 years old, making him one of the oldest, if not the oldest, being in the entire existence.
When the Valar sent the Istari to Middle-earth as their emissaries in the war against Sauron, they warned these angels to not use their raw strength in the conflict, only to influence the Free Peoples and push them towards the path of faithfulness. On top of whatever powers he may possess, Gandalf was given Narya, the Ring of Fire, by Cirdan the Shipwright when he made his landing on Middle-earth in 1000 TA. Galadriel holds Nenya, the Ring of Adamant, but going off the established lore alone, she’d be hard-pressed to stop Gandalf even with that, not that these characters have ever been pitted against each other, if only for the sake of nerding out.