promote

(verb) contribute to the progress or growth of. Synonyms: advance, boost, further, encourage. Example: "I am promoting the use of computers in the classroom."

(verb) give a promotion to or assign to a higher position. Synonyms: upgrade, advance, kick upstairs, raise, elevate. Examples: "John was kicked upstairs when a replacement was hired." "Women tend not to advance in the major law firms." "I got promoted after many years of hard work."

(verb) make publicity for; try to sell (a product). Synonyms: advertise, advertize, push. Examples: "The salesman is aggressively pushing the new computer model." "The company is heavily advertizing their new laptops."

(verb) be changed for a superior chess or checker piece.

(verb) change a pawn for a better piece by advancing it to the eighth row, or change a checker piece for a more valuable piece by moving it to the row closest to your opponent.