Paul, 36, missed the first two games of the series after entering the NBA's COVID-19 health and safety protocols on June 16 following a four-game sweep of the Denver Nuggets in the second round.
The Suns won both games in Paul's absence, including a thriller on Tuesday night in which Deandre Ayton stunned the Clippers with a last-second alley-oop dunk for the 104-103 victory.
Game 3 of the series goes Thursday night in Los Angeles.
Paul, a 10-time All-NBA point guard, has averaged 15.7 points and 8.7 assists to lead the Suns to the Conference Finals, shooting 51 per cent from the field, 44 per cent from three-point range and 91 per cent from the foul line.
-- With files from The Associated Press