dungeons and dragons – Is there any specific order to the four Elements when people talk about them?

There’s no official order for the elements in d&d.

I’m assuming that, in the typical d&d setting, a person knowledgeable of the planes and the cosmology might use the order in witch the 4 Elemental Planes appear, either clockwise (Air, Fire, Earth, Water), or anticlockwise (the opposite), with any element as a starting point. This however might be a personal preference of certain individuals / scholars, and is certainly not a rule in the lore.

edit: for reference in 5e, there’s a map of the planes at page 303, PHB.