The Governor's Office has written the following:
 
What the new law does:

Under the new law, Arizona's licensing boards will recognize out-of-state occupational licenses for people who:

Individuals seeking to work in occupations that require a background check will still need to complete those background checks. In addition, professionals receiving licenses under the new law can only become licensed in practice within areas they have been trained and certified to practice in their original state. Arizona licensing boards will be required to verify that an individual is in good standing in all states where they are licensed. Individual boards may have several pathways to licensure already in statute (interstate compact, licensure by endorsement, reciprocity, etc.). There are various pathways to licensure. Universal recognition is not meant to be the replace these pathways licensure, but represents an important new pathway that broadens the options available .

• Have been licensed in their profession for at least one year
• Are in good standing in all states where they are licensed
• Do not have any past or pending investigations or complaints
• Pay applicable Arizona fees
• Meet all residency, testing, and background check requirements per law

What the new law does not do:

The new law DOES NOT recognize other states’ occupational licenses automatically. For example, workers licensed in other states who move to Arizona still must apply for a license through the appropriate Arizona licensing board before working. However, under the new law, workers will not be required to duplicate training and other requirements that often needlessly delay or prevent them from getting to work.