It seems that the next jailbreak release will depend on three things - the finalization of iOS 10 with the issuance of version 10.3.3, Apple focusing on iOS 11 and the rumored leak of an iOS 10.3.1 exploit by security researcher Adam Donenfeld. The latter is happening around August, somehow hinting that a public jailbreak could come out within the month or early September.
Of course a jailbreak release in the immediate aftermath of the Donenfeld exploit revelation will only happen if the bug remains open for possible jailbreaking as Apple shifts its attention to iOS 11. And that should explain the August timing picked by Donenfeld for sharing his claimed KPP exploit. It is assumed that around that time iOS 10.3.3 has been finalized and the earlier firmware versions have been left open for tweaking, provided the bug hasn't been patched.
And there has to be jailbreak creators that will pick up the Donenfeld exploit as it was clear the security researcher will not be the one the assemble the jailbreak solution. On this, jailbreak fans hope Team Pangu will follow through on the demo they showed off back in April.
The Chinese hacking group has demonstrated that iOS 10.3 and iOS 10.3.1 can be jailbroken and the tool can be used on the 64-bit iPhone 7 series. Hopefully with the Donenfeld exploit, the devs will be able to complete what they have started.
Or it will be Luca Todesco that will step in but such a scenario seems bleak at the moment. Todesco has already indicated he's done with public jailbreaking and even made claims that after iOS 10.3 Apple's mobile OS will be impossible to jailbreak. But it might be the Donenfeld exploit could change the Italian hacker's mind.
In such a case, it's likely the jailbreak tool from Todesco or Pangu will appear between late August and early September or just before the deployment of iOS 11, which is to become public in the second or third week of the month.
However, there is also possibility that cannot be discounted. And that is any of the developers would want to check first if the Donenfeld exploit was carried over in iOS 11. That would mean it's more rewarding to work on an iOS 11 jailbreak than the older version of the software.