Short answer: you can't.
If your client really wants Orange 021, there is nothing in CMYK that will match their expectations. If you can't use a spot color, then I'd suggest going back to your client with a copy of the Pantone Process guide and have them pick a color out of it, or find a printer that will do the spot color.
That one, 021, like f.e. Reflex Blue use more pigments than just CMYK so you can not achieve the same color in process as in spot...
I don't really understand your answer and I don't think it's the one expected.
We can choose a pantone and convert it in CMYK. I know it's a color approximation but I think it's relevant.
OK, thanks. I guess another solution would be to use this pantone color in AI, convert to CMYK there and use the resulting color as a close version to the pantone. What is your opinion of this?
If the client asked specifically for Orange 021 (which is a very vibrant orange), I can't imagine that they would be pleased with even the closest CMYK substitution (which would be quite dull). That's why I suggested going back to the client with the Pantone Process guide for a new color choice if a spot color is not an option.
Thank you, I truly appreciate you sharing your expertise. The client absolutely liked that colour for it's vibrancy.
you can get the color from the color bridge which will give you the closest color to the pantone you want
but it will never give you exactly the same color
I guess another solution would be to use this pantone color in AI, convert to CMYK there
If you REALLY want to convert this PMS color to CMYK, you can do it directly in InDesign. Why do you want to add an AI step? But as SRiegel and others already said, you will loose the vibrant aspect of the Orange 021.
The client absolutely liked that colour for it's vibrancy.
If your client wants to match the color's saturation then it has to be run as a an extra spot color on press because Orange 021 is not in the standard CMYK color gamut. Doesn't matter how or where you make the conversion to CMYK because there isn't a formula that will match, and the legacy CMYK definition (0|53|100|0) wouldn't solve the problem.
I don't really understand the LAB colors we are forced to work with now....
The reason for the switch to Lab is the Pantone solid ink system was never intended to be used as a CMYK process color picker even though many designers try to use it that way. A large number of the colors are out-of-gamut and defining the colors as CMYK prevents the solid inks from being displayed accurately when they are being used as spots.
Photoshop's color picker will show when a solid ink is out-of-gamut.