The Romanian has been provisionally suspended since October 2022 after testing positive for roxadustat, a banned drug that stimulates the production of red blood cells, at the US Open that year.
Tennis anti-doping authorities also charged Halep with another doping offence last year due to irregularities in her athlete biological passport (ABP), a method designed to monitor different blood parameters over time to reveal potential doping.
Halep has vigorously denied the charges.
The former world number one has blamed contaminated licensed supplements for her positive test at the US Open. She has accused the International Tennis Integrity Agency (ITIA) of charging her with an ABP violation after the group of experts who assessed her profile learned her identity.
An independent tribunal accepted Halep's argument that she had taken a contaminated supplement but determined the volume she ingested could not have resulted in the concentration of roxadustat found in her positive sample.
The hearings at the Lausanne-based Court of Arbitration for Sport (CAS) are expected to run until Friday. The court said it was unclear when a ruling might be rendered.
Halep will attend the hearing in person but will not make any statements until the proceedings end, CAS said.
Halep told Euronews in December that if the court dismisses her appeal, she could be compelled to retire.
"It's catastrophic if it's going to be four years," she said. "I don't know how I will handle it. Probably it will be the end of my career."
