I'm on a realm world with seed -912478101. I create an Observer clock, at 258, 62, 259 and 259, 62, 259. The observer clock ticks about 5 to 10 times per second, inconsistently but like you'd expect.
If I then move to 251 62 260, I place another observer down on X=253, I can see the redstone light on for a long time – for about 20 seconds. If I put an observer in front of it (for the purposes of creating another clock), I'll continue seeing nothing for a while until the signal turns off on the new observer. Once the signal turns on on the new observer, it continues taking about 20 seconds to pulse, but that ALSO makes the other observer clock go slow. (Deleting those observers and replacing the first set allows them to pulse regularly again).
I don't have a lot in this chunk – maybe a dozen hoppers and a 40-or-so-high bubble column feeding into them. It's for a mob farm.
I took a video of it that I can make available, but it's 250mb and I can't upload it here.
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I figured out what the problem was. Ostensibly, it is still a bug. I'll update the title.
Someone in our world built a long ice road, but instead of using real ice / packed ice, he used Frost Walker. This created a long list of pending ticks, to determine if it was going to melt. Attached is the PendingTicks NBT list for chunk (15, 15, tag=51). The ice road goes within the X=15 chunk for quite a long way, and everywhere the ice road exists, there's massive redstone lag. Now that I've deleted all the ice in an offline world, all of the redstone lag is gone.
Ostensibly, frosted ice (especially just a 2-wide path, therefore 32 blocks per chunk) shouldn't create THAT MUCH lag.

Fixed in 1.13.0.1 beta