Note to myself so I do not have to figure that out every few month when I've to dig out a WLAN PSK from my existing configuration.

Step 1: Figure out the UUID of the network:

$ nmcli con show
NAME                  UUID                                  TYPE      DEVICE          
br-59d010130b86       d8672d3d-7cf6-484f-9ef8-e6ec3e73bef7  bridge    br-59d010130b86 
FRITZ!Box 7411        1ed1cec1-f586-4e75-ba6d-c9f6f4cba6e2  wifi      wlp4s0
[...]

Step 2: Request to view the PSK for this network based on the UUID

$ nmcli --show-secrets --fields 802-11-wireless-security.psk con show '1ed1cec1-f586-4e75-ba6d-c9f6f4cba6e2'
802-11-wireless-security.psk:           0815471123420511111