Second Display adds a display to the Mac you work on and sends what macOS draws there to the other Mac. macOS calls that recording the screen, so it asks you first.
Allow it
-
In setup, at Allow screen access, click Open System Settings… next to Screen Recording.
-
In System Settings › Privacy & Security › Screen & System Audio Recording (Screen Recording on macOS 14), turn on Second Display.
-
Go back to Second Display. If the row doesn’t say “Allowed” yet, click Quit & Reopen.
The recording indicator
While your screen is on the iMac, macOS shows a recording indicator in the menu bar. That’s expected, and it can’t be hidden. Newer versions of macOS may also remind you now and then that Second Display can record your screen.
Stopping the recording from that indicator disconnects the iMac. The menu then says “Stopped from the screen recording menu”, and Second Display doesn’t reconnect by itself. To get the picture back, turn the display’s switch on again in the Second Display menu.
If the permission is turned off later
The menu says “Screen Recording was turned off for Second Display.” and offers a button to System Settings. Turn it on again; if Second Display asks, quit and reopen it.
A locked screen isn’t a missing permission: while the Mac you work on is locked, macOS lets no app record its screen, and Second Display waits until you unlock it.