promote

contribute to the progress or growth of; "I am promoting the use of computers in the classroom"

give a promotion to or assign to a higher position; "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"

make publicity for; try to sell (a product); "The salesman is aggressively pushing the new computer model"; "The company is heavily advertizing their new laptops"

be changed for a superior chess or checker piece

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