Can I use a 2013 27 inch apple monitor as a duel with my new 2021 mac monitor?

Assuming this is in reference to the 24" iMac in your tag line, then it depends:

If the 2013 27" Apple Monitor is an actual iMac computer and not just a stand alone display, then no.

If it's a stand alone monitor then yes. You should be able to connect it the 24" iMac through one of the 24" iMac's Thunderbolt ports and and adapter to whatever connection the 27" monitor has. A 2013 Apple Thunderbolt Display would need a Thunderbolt 3/4 to Thunderbolt 2 adapter. click here ➡️ Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple

With the connection setup, you can set the 24" iMac to extend its desktop to the 2013 Monitor so you can use both as the desktop for the 24" iMac.

click here ➡️ Use one or more external displays with your Mac - Apple Support

Pretty much any monitor will be compatible with it. Most through the use of an adapter.

LG makes good quality displays.

https://www.lg.com/us/4k-monitors