In May, Mr Trump was found liable for sexually abusing Ms Carroll in the 1990s and defaming her after she went public with her allegations in 2019.
The former president continues to say Ms Carroll made up a “fake story”.
Awarded $5m (£4m) in damages at the first trial, the ex-Elle magazine columnist now seeks a further $10m.
During jury selection on Tuesday, accuser and accused were in the same room together for what appeared to have been the first time in more than two decades.
Though Mr Trump, 77, was deposed in the earlier trial, he did not attend in person or testify, both of which he is doing voluntarily in these proceedings.
Ms Carroll, 80, has said Mr Trump forced himself on her inside a Manhattan department store in the 1990s after a chance encounter with the property tycoon.
Her accusation, first published in New York magazine in June 2019, was rebutted by Mr Trump from the White House as a “con job” and a “hoax”.
The Republican president used “the world’s biggest microphone to attack Ms Carroll, to humiliate her and to destroy her reputation”, an attorney representing her said in opening statements on Tuesday.
Shawn Crowley told the court Mr Trump had “unleashed” death threats, rape threats and online vitriol that caused her client “to live every day in fear”.
Calling on jurors to assess both “how much money Donald Trump should have to pay for what he’s done” and “how much money it will take to make him stop”, Ms Crowley called for a “very significant” sum of damages.
But Alina Habba, Mr Trump’s lead attorney in the case, argued on Tuesday that Ms Carroll did not deserve damages because her accusation of sexual assault had made her famous.
“Evidence will show you her career has prospered and she has been thrust back into the limelight Iike she always has wanted,” Ms Habba said.
“She likes her new brand, and she has been monetising it for years,” she added.
Mr Trump, who also faces 91 felony charges across four criminal cases this year and is awaiting judgment in a New York civil fraud trial, is currently the Republican frontrunner for president.
On Monday, he scored a resounding win – with a record margin of victory – in the Iowa caucuses, the first of the state-by-state contests in the race to become the Republican party’s White House candidate.
His presence in court on Wednesday comes as he is ramping up campaign appearances in New Hampshire, where the second contest takes place next Tuesday.
He has repeatedly said he “knows absolutely nothing about” Ms Carroll, including in more than a dozen posts on his Truth Social platform as he attended Tuesday’s hearing.
Mr Trump is expected to testify in the trial on Monday.
