Plastic ID card printers come in two types: dye-sublimation and thermal re-transfer.  Either one of these printers can be used to print a photo ID on a plastic card, however the quality of the dye-sublimation printing will be significantly inferior to the quality of the thermal retransfer printer.  The cost of dye sublimation printers, and associated software and supplies, is generally under $5,000.  The cost of thermal retransfer printers is generally closer to $10,000.  Anyone can acquire these machines over the internet from specialized re-sellers.  The learning curve may be steep, and it may take a number of trial-and-errors to get it right.  But with the right skills, and adequate financial resources, it can be done.

A far easier way to get professional photo ID cards on plastic credit-card style cards is to use a specialized service such as InstantCard. Here is a good guide for determining alternative sources for your ID cards: https://instantcard.net/increase-quality-and-efficiency-with-instantcard/.  For less than $10.00, you can get a high-quality card printed with the best thermal retransfer technology.  And you get the assistance of ID card professionals, whose business it is to design and manufacture secure ID cards.  These web services have invested heavily in the technology to produce top-quality cards at a reasonable price.  They provide a much more cost-effective way of getting a photo ID on plastic ID cards.

Along with your ID badge program, you should consider publishing a policy on the use of those badges.  A good source for an initial standard policy is the Society for Human Resource Management suggestions at https://www.shrm.org/resourcesandtools/tools-and-samples/policies/pages/id-badge-policy.aspx.