Answer by taking a quote from the following article:

Hooper was born on August 24, 1887, in Bell Station, California. His family had migrated to California as many other families from the United States due to the California Gold Rush. His father, Joseph "Joe" Hooper, was born in Morrell, Prince Edward Island in Canada. Joe was the fourth child and second boy born to English-born William Hooper, Harry's grandfather, and his Portuguese wife Louisa.

Before the 1921 season, the media questioned whether Hooper would re-sign with the Red Sox for the coming season, saying that Hooper may have been disappointed not to be given an opportunity at manager. Since 1919, Red Sox owner Harry Frazee had been getting rid of expensive veteran players in what has been called a "fire-sale". Hooper was traded to the Chicago White Sox in March 1921 in exchange for Shano Collins and Nemo Leibold. Newspaper accounts said that Hooper had not been warned about the trade, that he would demand a higher salary from the White Sox and that he was prepared not to play unless the team met his demands.  Hooper had some of his best offensive production with the White Sox. He hit over .300 in three out of the five seasons he spent with the team and he hit a career-high 11 home runs and 80 runs batted in during the 1922 season. In 1922 and again in 1924, Hooper was involved in eight double plays, which led the league for outfielders in both of those seasons. In 1925, Hooper asked for his release from Chicago so that he could pursue a position as a manager.  Hooper was a career .281 hitter with 75 home runs, 817 RBI, 1429 runs, 2466 hits, 389 doubles, 160 triples, and 375 stolen bases in 2309 games. He holds the Red Sox franchise records for most triples (130) and stolen bases (300), as well as Fenway Park records for triples (63) and stolen bases(107). Hooper is only one of two players (Heinie Wagner being the other) to be a part of four Red Sox World Series championships. He hit better than .300 five times in his career and compiled a .293 batting average (27-92) in four World Series appearances.

Was Harry Hooper a good White Sox player?
Hooper was traded to the Chicago White Sox in March 1921 in exchange for Shano Collins and Nemo Leibold.