Elves will be made right after the dwarves altough they don't wear much in terms of mail in the silmarillion. At most they are described as wearing just a little, for the most part gaining their protection from their lightning reflexes and shields.
As Luke Ueda-Sarson says:
Noldorin forces were generally a mixture of cavalry and infantry. Cavalry was quite numerous (Sil, p147), although prior to the founding of the princedoms, horses were few (Sil, p141). Some charged swiftly (Sil, p230), but most were horse archers (Sil, p138, 193). Charging cavalry are assumed to be those that carried spears (Sil, p213); they are graded as Kn (F) since even the highest nobility used mail which is never mentioned as being 'full', unlike that of the knights of Gondor (eg. Sil, p184).
The dwarves are being made right now. They will be command, nobles in heavy armour with axes, warriors with axes, warriors with various melee weapons, and archers.