adding a monitor

Well the imac will not support Target Display Mode, that functionality was only available on late 2009 27" iMacs through 2014 iMacs. So because you have a 2017 iMac it simply will not work. Therefore if you need an external display for your 2012 MBA then you need to buy one.

MBA is MacBook Air

To learn what computers you own, please click the Apple symbol in the upper left of the display and then click About this mac. The window that pops up will tell you the year of each device. For example, Late 2009 27" iMac

Is the monitor plugged in? Are you seeing anything on it?

Are you mirroring rather than extended desktop?

Use external monitors with your Mac - Apple Support

Then you must be specific, what year iMac do you have and what year MBA do you have?

I cannot find the article at the moment, but it critically depends on what macs you have.

Just go to "about this mac"

Your other computer. MacBook Air.