Connect to iMac (macOS Monterey) an external apple display

That Mac has two USB-C (Thunderbolt 3) ports.

iMac (21.5-inch, 2017) - Technical Specifications - Apple Support (PH)

You haven't indicated which 27-inch Apple display you are trying to use.

• The 27" Apple 5K Studio Display which Apple currently sells would plug right into one of your Thunderbolt ports. Your iMac is the low-end one which only has two CPU cores, and no discrete GPU – so I don't know whether the performance would be too great. But technically your iMac is compatible with that display.
• For the 27" LED Cinema Display, you would need a USB-C (male) to Mini DisplayPort (female) adapter. The 27" LED Cinema Display has a "hydra" cable with three heads: Mini DisplayPort, USB, MagSafe. You would need to plug in the USB head if you wanted to be able to control the brightness of the display.
• For the 27" Apple Thunderbolt Display, you would need an Apple Thunderbolt 3-to-2 adapter. The Thunderbolt Display has a "hydra" cable with two heads: Thunderbolt (Mini DisplayPort connector), MagSafe.

Is that an Apple Thunderbolt 3-to-2 adapter?

You need that adapter for a 27" Apple Thunderbolt Display. That adapter won't work for a display like the 27" LED Cinema Display. Unlike a TB2 host port on a Mac, the TB2 port on that adapter does not double as a Mini DisplayPort. The only thing the TB3-to-2 adapter translates is Thunderbolt.

Check the hydra cable of that 27" 2560x1440 Apple display. If it has three heads, it's not a Thunderbolt Display, and what you want is a much cheaper USB-C (male) to Mini DisplayPort (female) one (several on Amazon).