The Ainur in Arda (i.e Valar and Maiar) are bound within the world until its end, per the Ainulindale:
But this condition Ilúvatar made, or it is the necessity of their love, that their power should thenceforward be contained and bounded in the World, to be within it for ever, until it is complete, so that they are its life and it is theirs.
However, they don't have physical bodies:
...their shape comes of their knowledge of the visible World, rather than of the World itself; and they need it not...
So it's incorrect to speak of them physically aging and the answer to your question is therefore "no".
The exception to this rule is, of course, the Istari, who were bound in physical bodies (that could even be killed) as part of their mission; Of the Rings of Power and the Third Age notes:
In the likeness of Men they appeared, old but vigorous, and they changed little with the years, and aged but slowly, though great cares lay on them...
Otherwise it's certainly true that they can spiritually age, however, and Tolkien makes occasional reference to this kind of aging for the Elves too, commonly using the word "weary" to represent it. See for example the story of Miriel in the Silmarillion. The Second Prophecy of Mandos (omitted from the published Silmarillion on the basis of evidence in the Valaquenta) contains a reference to the Valar growing weary at the end of the world.