If you hold a Private Pilot License (PPL) you can fly an aircraft for your own personal use such as flying for fun travelling with friends or family or building flying experience. But you cannot fly and earn money by carrying passengers or cargo for hire. According to the article How Is a CPL Different from a PPL the PPL is strictly for non commercial recreational flying.
In other words you can't use a PPL to fly commercially. A commercial flight means you are getting paid for the service like being hired as a pilot or carrying paying passengers or cargo. The article clarifies that only the Commercial Pilot License (CPL) allows you to fly professionally and earn money.
Here are some key things the article mentions that differentiate PPL and CPL (and help answer your question):
Under the Privileges and Limitations section: For a PPL the main purpose is flying for hobby learning or personal enjoyment and there is no income allowed from flying. For a CPL the main purpose is flying professionally and earning money.
The Type of Flying row shows that with a PPL you can do Personal recreational non commercial flights, whereas a CPL allows Commercial charter airline and professional flying.
The article states clearly: PPL is for personal flying while CPL is for building a paid career as a professional pilot worldwide.
So, when can someone with a PPL fly commercially The answer: Never unless they upgrade to a CPL (and meet all the additional requirements). Simply having a PPL is not enough to legally fly commercially. You must obtain a CPL and usually meet additional flying hours exams medical requirements etc. to fly for hire or reward.