Direct one’s hopes or ambitions towards achieving something.

we never thought that we might aspire to those heights

desire,desire to,aim for,aim to,hope for,hope to,long for,long to,yearn for,yearn to,hanker after,hanker for,hanker to,set one’s heart on,wish for,wish to,want,want to,expect,expect to,have the objective of,dream of,hunger for,hunger to,seek,seek to,pursue,have as one’s aim,have as one’s goal,set one’s sights on