conky configuration (.desktop files in ~/.config/autostart/)

conky-monitor-change.desktop

[Desktop Entry]
Exec=~/Workspaces/monitor_change.py
Name=Conky Automatic Restart
Comment=Run Conky automatic restart on monitor change
Type=Application
Icon=video-joined-displays-symbolic
NoDisplay=true

conky.desktop

[Desktop Entry]
Exec=conky
Name=Conky System Monitor
Comment=Run Conky system monitor
Type=Application
Icon=conky-manager
NoDisplay=true

monitor_change.py

#!/usr/bin/env python3
import subprocess
import time

def get(cmd): return subprocess.check_output(cmd).decode("utf-8")
def count_screens(xr): return xr.count(" connected ")

# first count
xr1 = None

while True:
    time.sleep(5)
    # second count
    xr2 = count_screens(get(["xrandr"]))
    # check if there is a change in the screen state
    if xr2 != xr1:
        subprocess.Popen(["/usr/bin/pkill", "-f", "conky"])
        time.sleep(5)
        subprocess.Popen(["/usr/bin/conky"])

    # set the second count as initial state for the next loop
    xr1 = xr2