Nozdormu himself makes a reappearance between the Second and Third Wars, being one of the Aspects who bands together to free Alexstrasza and defeat Deathwing. He's also involved in the events wherein Korialstasz/Krasus, Rhonin, and Broxigar are sent back in time and completely confuse the heck out of everyone reading along trying to figure out the original events of the War of Ancients vs. their changes and alterations. Good job there, Nozzie. That helped keep those timelines straight.
Since then, the various sub-factions of the Bronze Dragonflight (the Brood of Nozdormu, the Keepers of Time, and the Scale of the Sands) have each seemingly taken on specific duties. The Brood, led by Anachronos, seems most concerned with protection the Bronze Dragonflight itself, stopping the Qiraji once and for all and otherwise making sure the other factions continue their work unmolested. The Keepers of Time (led by the brother and sister pair Andormu and Nozari) seem more directly involved with the actions of the Infinite Dragonflight, a group of strange dragons and draconids who work to alter the timeline for some as yet unknown reason (which I will be going into next week) and the Scale of the Sands serves as Soridormi's personal servants, currently occupied with trying to preserve the timeline around the events of the Battle of Mount Hyjal.
At present (as much as that word has any meaning to a group of time travelers) much of the bronze dragon's efforts are taken up in their conflict with the infinites. It's impossible to say when this conflict actually started. For all we know, the Infinite Dragonflight won't even come into existence for thousands of years. Since both they and the bronzes are capable of moving through time, their skirmishes take place on a constantly shifting battlefield of when, not where. We do know that even during the Nexus war Chromie sends adventurers to the Bronze Dragonshrine in Northrend, where selected agents team up with themselves twice in order to do battle with the infinites and see a puzzling image of Nozdormu at the end of a rite that is intended to show the leader of that time altering faction.
Chromie reveals at the end of that quest (the first quest, where future you comes back to help present you in the dragonshrine, not the second quest, where present you goes back in time to help past you defend the dragonshrine) that the bronzes currently have no idea when Nozdormu is, merely that he's away dealing with important temporal matters. However, since the rite she sent you to enact was intended to determine who the leader of the infinite dragonflight is, quite a few have theorized that this means Nozdormu is in fact the head of the infinites. How could the Aspect of Time, in charge of maintaining the timeline, dedicate himself to destroying it? Well, there are many possibilities, none confirmed.
- It's not Nozdormu at all, and Chromie was right, the hourglass did indeed show Nozdormu fighting back against them.
- It's a future alternate version of Nozdormu seeking to prevent his own death reaching back in time to change events on Azeroth so that he won't die. He's disabled his 'present' self so he won't fight him.
- It's present day Nozdormu doing the same thing, but because he knows he's supposed to. His awareness of the time and place of his death indicates he dies because he starts the infinite dragonflight, so he did so in order to preserve the timeline and bring out the foreordained events of his foreseen death.
- Nozdormu has gone mad because he has to maintain the sanctity of a timeline that leads inexorably to his own death, which he knows the exact date and means of, so his personality has broken and he isn't even aware that he's the head of the infinite dragonflight.
- It's not Nozdormu, but someone close to him that either wants to usurp his position or prevent his death against his own will (Soridormi and Anachronos would both be contenders here) - Nozdormu is either being kept out of the loop or actively subverted by his most trusted followers.
- Come up with your own crazy theory! It's time traveling dragons, it doesn't have to make a whole lot of sense.