Converting from one color standard to another

I am looking for help. Over the years I have been running to a color standard developed in house. This has worked well, and I have been keeping a library of CMYK images tagged with the ICC profile of this in house color standard.

I would like to change to another color standard. The reason for the change is the library of images are now being used outside. And I will still be adding to the library for the next 5 years.

I have found some of the outside printers do not value my in house standard, so I am deciding to change to a more acceptable color standard for universal use.

How do I take the library I have now and convert them over to the new color standard? I am looking for the most cost effective way.

Thanks in advance for your suggestions.