Particularly in the Hobbit movies, Elrond mentions that Gandalf answers to Galadriel. Though Gandalf is a Maiar, one of Ainur, shouldn't he be regarded as one of the elders one above the Noldor?
One of the opening paragraphs of "The Istari", an essay printed in Unfinished Tales, largely answers this (emphasis mine):
[The Wizards] came from over the Sea out of the Uttermost West; though this was for long known only to Círdan, Guardian of the Third Ring, master of the Grey Havens, who saw their landings upon the western shores. Emissaries they were from Lords of the West, the Valar, who still took counsel for the governance of Middle-earth, and when the shadow of Sauron began first to stir again took this means of resisting him. For with the consent of Eru they sent members of their own high order, but clad in bodies of as of Men, real and not feigned, but subject to the fears and pains and weariness of earth, able to hunger and thirst and be slain; though because of their noble spirits they did not die, and aged only by the cares and labours of many long years. And this the Valar did, desiring to amend the errors of old, especially that they had attempted to guard and seclude the Eldar by their own might and glory fully revealed; whereas now their emissaries were forbidden to reveal themselves in forms of majesty, or to seek to rule the wills of Men and Elves by open display of power, but coming in shapes weak and humble were bidden to advise and persuade Men and Elves to good, and to seek to unite in love and understanding all those whom Sauron, should he come again, would endeavour to dominate and corrupt.
Unfinished Tales Part 4 Chapter II: "The Istari"
From the above paragraph, the answer has two related parts:
The Elves don't defer more to Gandalf because they don't know what he actually is. It's not entirely clear what the Elves do think Gandalf is, but it seems safe to say that they would be more deferent if they knew he was one of their Angelic spirits.
Gandalf is forbidden from setting himself above them. This is Saruman's great failing, incidentally: the Wizards are meant to be teachers and counsellors only, not rulers. So from that perspective, it's not true that Gandalf is higher than the Noldor; he may be of a higher order of being, but within Middle-earth he's merely an advisor
Now that the real stuff is out of the way, let's move on to the films. The specific exchange from An Unexpected Journey is:
Gandalf: With or without our help, these dwarves will march on the mountain. They are determined to reclaim their homeland. I do not believe Thorin Oakenshield feels that he’s answerable to anyone. Nor for that matter am I.
Elrond: It is not me you must answer to.
[Galadriel turns around]
Gandalf: Lady Galadriel.
The Hobbit: An Unexpected Journey (2013)
There is, of course, no sensible reason why Gandalf should have to answer to Galadriel alone; although he doesn't command her, equally she doesn't command him.
Unfortunately I don't believe an official script has been made available, so there isn't likely to be a canon explanation of Jackson's intentions here. However, the most sensible explanation is that Elrond is referring not to Galadriel, but to the White Council.
I discuss the nature of the White Council elsewhere on this site, but the gist is that they are a loosely-affiliated group of powerful beings (including Gandalf, Saruman, Elrond, and Galadriel) who coordinate their efforts to counter the advances of Sauron. This is the one group in Middle-earth for whom it might be sensible to say that Gandalf "answers to."
My interpretation, then, is that Elrond's line and the subsequent appearance of Galadriel isn't meant to convey "Gandalf answers to Galadriel", but rather that Galadriel's presence changes the nature of the conversation; rather than a discussion between disagreeing friends (Gandalf and Elrond), it has turned into a meeting of the White Council, and it's to them that Gandalf must answer.
Could it be because Galadriel and Elrond are fellow ringbearers ?
It can be explained with some common sense and basic diplomacy: Galadriel and Elrond are Kings and they (and their subdits) are used to that reverence. They are also powerful allies (both as ring bearers and rulers of their Kingdom).
Apart than it would be out of character for Gandalf (who prefers not to act directly as long as he can avoid it) to break protocol just to brag about how powerful he is, the only possible benefit of such an action would be aleniating his allies. Even if Elrond or Galadriel put up with him, their subjects probably would not understand that they allow such a behavior in a foreign "newcomer". Not what any sensible character would do, and much less a nice one.
Note that Gandalf also shows respect to the human kings, and while he may disagree with some of their decisions, he avoids disobeying them (the only exception I recall was with Denethor's demise). Even when Gandalf disagrees with Denethor's orders to send Faramir against Osgiliath, he does nothing to prevent that.
In addition to their wisdom, leadership and historical roles, both Galadriel and Elrond have deep historical significance.
Galadriel was born in Valinor, and remembers all the ages of world since the light of the Two Trees. In addition, she is described as having among the mightiest spirits of among the Elves... on the same order as Feanor (he who made the Simarils and captured the light of the Two Trees). Finally, as other answers have noted, she bears one of the three Elven rings. So if Elves are worth revering, she is basically more worthy of reverence than almost any elf in the history of Middle Earth.
Elrond is a survivor of the tragedy of the Noldor and of Beleriand at the end of the First Age, and is among the first beings descended from Elves, Men and Melian the Maia. He is descended from Huor and from Beren on the human side, and from Indis, Olwë, Thingol and Finwë on the elven side. So in Elrond lives the legacy of the best of Elves and Men, and there's that whole angelic/demigod Maia thing. Finally, Elrond too, is one of the elven ring bearers.