The team on Tuesday exercised its third-year options on both players.
Shamet was acquired by Los Angeles in a midseason trade with Philadelphia last winter. He's averaged 9.2 points and shot 42% from 3-point range since being selected with the 26th pick in the 2018 NBA draft.
Robinson, the 13th overall pick in the 2018 draft, was dogged by a foot injury during his rookie year that kept him mostly with the Clippers' G League affiliate in nearby Ontario. He averaged 18.9 points and 4.2 rebounds there.
He's averaged 3.2 points on 40% field-goal shooting in 36 regular season NBA games.