Convert Corel to in Adobe Illustrator?

It's often pretty tricky and problematic moving artwork and page layouts bewteen CorelDRAW and Adobe Illustratror. The problems are compounded if you have use of only one of those applications and depend on clients to "fix" files they're providing. The two applications have a certain amount of feature overlap, but also many unique differences that just don't translate to the rival application. Even basic things like text objects in CorelDRAW files can go all wonky when imported into Illustrator via either an ancient version CDR file or an AI file exported from CorelDRAW. Our sign company has to use both programs extensively. CorelDRAW is very popular in the sign industry. But we do a great deal of large format printing work and Illustrator, InDesign and Photoshop are better on the front end for that. Plus we deal with brand resources from many major companies and virtually none of those assets comes in CorelDRAW format. It's almost always Illustrator AI, EPS and PDF files.

Are your clients sending CDR files or exported AI files? Also which application versions are they using? I usually get better results sending Corel-generated artwork to Illustrator as an exported AI file. I usually finalize any live application-dependent effects prior to file export. Illustrator's CDR import functions are frankly pretty lousy. Generally chances are better for a later version of CorelDRAW, such as CDR 2018 or 2019, to be able to export an AI file that doesn't turn to garbage when opened in Illustrator. In addition to the CDR or AI file they might provide they'll probably have to include a PDF (that they proof for accuracy in Adobe Reader) so you can see how the fills and effects are supposed to look. Corel-generated PDFs aren't very import-friendly to Illustrator. Even Astute Graphics' Vector First Aid plug-in won't fix all the problems.

Accurate translation of object fills (gradients, transparency effects, etc) has long been a problem between the two applications, but that situation has improved somewhat in recent versions of CorelDRAW. IIRC CorelDRAW X8 was the first version that could import AI files without gradient fills getting botched (it's still not perfect though). CDR 2018 allowed levels of transparency to stops on gradient fills.

Corel's Font Manager application can add another level of headaches for any Illustrator user trying to open/import CDR files. CorelDRAW users can create layouts using fonts not installed in the operating system. In recent updates of Windows 10, such as the Fall Creators Update, native support for Postscript Type 1 fonts has been removed. I find that especially annoying since I have quite a few very good yet vintage T1 fonts, such as the Akzidenz Grotesk BE family that came with the copy of Illustrator 4 I bought back in the early 1990's. Anyway, those old T1 fonts can still be used in CorelDRAW, but with some odd catches. They'll print to our office printer from CDR 2018 or CDR X8, but don't print at all from CDR 2019. And the Postscript T1 fonts don't show up at all when exported to Adobe Illustrator. You can try installing the T1 fonts into Windows' Fonts folder but they won't show up in Illustrator; then when you re-boot the computer those T1 fonts will be removed from the Windows Fonts folder.

If they start in Corel, do editing in Corel. Save as interchange graphics once final. It’s pointless and damaging to force work into your preferred editor before it’s ready.