You need to use the variable ${addr enp4s0} in your .conkyrc or whatever file you use for configuration of the display; here's what I have in mine with the up and down speed-graph boxes which you may find useful as well
Code:
NETWORK IP: $alignr enp4s0 - ${addr enp4s0}
DOWN: ${downspeed enp4s0}/s$alignr UP: ${upspeed enp4s0}/s
${color #FFA500}${downspeedgraph enp4s0 40,158}$alignr${upspeedgraph enp4s0 40,158}
The screenshot is of the output this gives me.
EDIT:
Sorry; just noticed this is about external IP.
I think your command will do this and you need to run it and extract the output to the conky display with
Code:
PUBLIC IP ${alignr}${execi 60 curl ipinfo.io/ip}