An Apple authorized service provider should be able to upgrade the RAM for you; it involves a take-part.
The 'Late 2013 21.5-inch iMac' memory specs - are as follows from http://mactracker.ca database app
Better to get both replaced, if you are paying to have a tech open the iMac for you. If they are installing
quality sourced memory RAM chips from reputable manufacturer, guaranteed, 16GB is recommended.
• Find an Apple Authorized Service Provider
Built-in Memory 8 or 16 GB PC3-12800 (1600 MHz) DDR3
Maximum Memory 16 GB
Memory Slots 2 - 204-pin PC3-12800 (1600 MHz) DDR3 SO-DIMM (Non user-accessible)
While the computer is open for upgrade, you may consider matching memory chips for best performance
and then they would not need to be upgraded later. When at an AASP you may ask about other upgrade
possibilities they could perform for you in your iMac 21.5, beyond the memory RAM chips.
Good luck & happy computing! 🙂