WordNet sense 1 (something added to what you already have):

addition

WordNet sense 2 (agreeing with or consenting to (often unwillingly)):

assenting

WordNet sense 3 (the right to enter):

access, admittance, entree, entrée

WordNet sense 4 (the act of attaining or gaining access to a new office or right or position (especially the throne)):

rise to power