I want to buy a refurbished 27" apple monitor with Thunderbolt 1 connection and connect it to my new 24 " iMac. will this work?

Yes, but resolution will limited in the 27" Thunderbolt display.

You will need a USB-C / Thunderbolt 3 to Thunderbolt adapter: link-> Thunderbolt 3 (USB-C) to Thunderbolt Adapter - Apple

blue diva wrote:

the back of the iMac has USB 3 and thunderbolt/usb 4

Yes, this adapter will work with that: Thunderbolt 3 (USB-C) to Thunderbolt Adapter - Apple

Unless someone has tried this, I don't know that you will get a definitive answer. However, you will need a TB1 to TB3 adapter.