My guess is that it'll either be "right after this Nintendo Direct" or "A week after this Nintendo Direct."
Given that we've run out of new maps, I expect the patch to be soon, so early August. They usually have Directs on the first week or last week of the month. Since I expect new content soon, I expect an early August Direct. Now, we need to think "What day of the week do they usually do Directs on?" They're usually on Tues, Wed, or Thur.
Basically, I think we'll get a Direct on August 4th, 5th, or 6th that will announce a Splatoon update directly after, or very soon after.
The spanner in the works here is that Smash is ALSO getting a big August patch. While I think it's less likely it'll be directly after the Direct, I do think they'll try to space them out, to keep people from downloading both updates and clogging up their online infrastructure. So, that could throw things off a bit.
But, yeah. That's my logic. I'm going to guess AUGUST 4TH, or near it.