WASHINGTON—Gathering in the aftermath of President Trump’s impeachment, seven Democrats will seek to gain an advantage in the unsettled race for the presidential nomination in a Thursday night debate promising to offer the contest’s last big inflection point of the year.

The Democrats squaring off in Los Angeles have been largely united over Mr. Trump’s impeachment, which now moves to a Senate trial that likely will command attention in the weeks before the Iowa caucuses on Feb. 3.

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