Typically the first step with a sync problem is to determine that the reminders (or whatever data is failing) is getting to the cloud but we know this is happening because the reminders are getting to your new computer. That means we can move to the second step.
Close Reminders if it is open. Open System Preferences and select Apple ID. You’ll see a list of Apps that use iCloud. Find Reminders and click the checkmark off then close the System Preferences app. Wait a minute or so and then return to the Apple ID tab and click on the checkmark to sync Reminders. Again close preferences, wait about a minute and then check to see if Reminders synced. My experience is this works about 1 time out of 5 but is less drastic than step 3 so give it a try before moving on below if necessary.
Step 3 is to log out of iCloud entirely which is done back at the Apple ID tab of system preferences. When you attempt to log out you’ll be asked if you want to leave a copy of all the synced data on your Mac. No, because after a minute you’ll log back in to (hopefully) resume syncing everything. So choose no, go ahead and log out - this will take a minute or two because the computer will be removing data from your computer - no worries - it remains in the cloud. Once it is finished and you are logged out you then log back in and your data will sync. Again, this process will take a couple minutes because it has to download all your synced data - calendars, contacts, etc. This almost always works but since it takes a while I don’t generally jump to it right away.