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Mac or PC? And which version of InDesign?
Mac. Using InDesign 2021 (16.2.1)
Rob Day's answer below will get you where you want to be.
when on Windows 10 you could visit:
[USERNAME] > AppData > Roaming > Adobe > Color > Profiles
( If folder Profiles does not exist, create one. )
Store the ICC profile for your new destination there.
Restart InDesign and try again.
( ACP )
I'm on a Mac. Using InDesign 2021 (16.2.1)
It looks like your Export is to PDF/X, is the Destination profile you are looking for a CMYK or output class profile? PDF/X doesn’t allow RGB display destinations. On OSX copy profiles to:
Startup HD ▸ Users ▸ username ▸ Library ▸ ColorSync ▸ Profiles
Startup HD ▸ Library ▸ Application Support ▸ Adobe ▸ Color ▸ Profiles ▸ Recommended
which should put the profile at the top of the Destination list
That's it. Thanks.