Do you have Finder configured to display mounted volumes on the Finder's Sidebar? You can also select "Computer" from the Finder's "Go" menu which should also show you any mounted volumes.
Is the external drive even mounted? Check Disk Utility to see if the external drive is mounted or even physically seen. Within Disk Utility you may need to click "View" and select "Show All Devices" before the physical drives appear on the left pane of Disk Utility. Sometimes an external drive may need to be manually mounted using Disk Utility (especially if the drive is encrypted).
Is the external drive connected directly to the new Mac?
Does the external drive have its own dedicated power supply?
Try disconnecting all other external devices in case one of them is causing a problem.
Try booting into Safe Mode to see if you can access the external drive. If the external drive is using NTFS and you have any third party NTFS drivers installed, then you may not be able to access the NTFS volume while booted into Safe Mode since those third party drivers may modify macOS settings to only allow the use of the third party drive which would be disabled in Safe Mode.
Maybe the USB adapter or cable being used with the external drive has an issue.
Perhaps the external drive is not receiving enough power and either requires its own power adapter, or perhaps a powered USB3 hub can be used to give the external drive more power.
Is the new iMac an Intel or M-series Mac?
What is the exact make & model of this external drive?
And what file system is on the external drive?
Were you using any third party software to manage this external drive on the broken iMac?