There's a lot to be done, in the immediate aftermath of finding Carissa and young Ma'ar in Urtho's Tower, and for a while Leareth is very very busy, as well as very happily distracted in his scant free time by having his wife back. And Ma'ar needs lessons, in magic and other things, and he has a baby daughter and spends more time than he strictly needs to visiting the nursery to hold her.
He introduces Ma'ar in the palace as a 'relative' who's going to be fostering here with him and Carissa for the next few years; he doesn't try to further explain the situation. There are curious whispers and various rumours about this for a little while, but then it stops being controversial.
Running Cheliax continues to hold many ongoing headaches. There are nobles used to getting away with more than he especially wants to let them; there are a handful of local insurgencies that need dealing with, and uncertainty around whether there's any larger organization behind this; some neighbouring countries are still discomfited by the rapid changes of the last year. But nothing goes sufficiently wrong to reach the threshold of being an emergency, rather than just a hassle.
They try a Sending to the other Velgarth he found, but it doesn't work, maybe 'the Leareth who lives there' isn't specific enough, and even after consulting his records he hasn't been able to narrow down what name he was going by or what he was doing at the time.
After six months, he finds time to slip off with Urtho and return to the Velgarth of a millennium ago, and check the cache where he left a note for his younger self. There's no reply, which is unsurprising - even over the entire course of a given lifetime he won't necessarily visit all of them - but in the meantime he's looked up the locations of a dozen other records caches, spread around the world. He leaves more notes.
Another six months later, there are still no replies. This time he brings a Chelish wizard with him too, to attempt a Sending from within the same world; this doesn't work either.
After that point, he stops going in person, and sends one of his mages every so often, equipped with a map and a list of locations to check, plus knowledge of the counterspell-techniques to his protective wards. Someone who's travelled widely throughout their Velgarth and can manage Gates to places that haven't changed too much, and compensate with scrying for the differences across a thousand intervening years.
At the two-year mark there's still nothing. Leareth worries about this a little, and then puts the matter out of his mind; the very fact that this is taking place during a gap in his records, and that there are no large-scale activities that hint at his presence, means it's not as time-sensitive as many of the other things on his plate.
He still sends another mage a year later, though, with the same briefing, a list and a map.