Typically new crown crates are released a week or so after the next dlc comes out. I'd expect a week after this year's chapter drops. But they usually let you know when they're about to be gone anyway.
II Blinkin II
Xbox 1 NA
"A man without the sauce is lost, but the same man can become lost in the sauce."
Xanmeer Crown Crates season started on December 6, 2018.
Dragonscale Crown Crates season started on March 28, 2019.
Usually a crown crate season lasts about 3 and half months or a bit more.
We can expect the next Crown Crate season to be released in late June(probably the "Baandari" season).
A link for more information: https://en.uesp.net/wiki/Online:Crown_Crates
Main character: PC EU main: Universe - AD magicka Sorcerer, Former Emperor, Grand Overlord, The Merciless, Trial Bosses Solo Champion
Top alts: Genius(stamina/sagicka Dragonknight) The Force(stamina Nightblade) and other chars. PC NA main: The Magic - AD magicka Sorcerer
Started playing ESO in beta & early access User_ID: Daedric_Prince