The popup opens but nothing pastes
Work down this list; the first item fixes it most of the time.
Updated
Accessibility access is missing or stale
Maclip pastes by sending ⌘V, which needs Accessibility access. Even if the switch looks on, reset it as described in Grant Accessibility access.
A password field or Secure Keyboard Entry is active
While a password field has focus, or Terminal has Secure Keyboard Entry turned on (in the Terminal menu), macOS blocks keystrokes sent by other apps. Click into a normal text field, or turn Secure Keyboard Entry off.
Nothing happens when you press the shortcut
Another app may already use that combination. Pick a different one in Settings → Keyboard Shortcuts & Access.
Workaround: copy, then paste yourself
If one app refuses pasted keystrokes, open the clip in the dashboard, copy it, and press ⌘V in that app.