to contribute to the growth or prosperity of (something)

to help bring (e.g. an enterprise) into being

to present (e.g. merchandise) for public acceptance through advertising and publicity

to contribute to (something) in a beneficial way

Regular exercise promotes good health

to cause (somebody) to advance in position, rank, or status

to assign (a team) to a higher division of a sporting competition, e.g. a football league: compare relegate

in chess, to change (a pawn) into a more valuable piece when it reaches the end of the board

NAmer to cause (a student) to move to a higher class or grade