こんにちは。 「返り咲く（かえりざく）」is dictionary form. ex: 彼（かれ）はその試合（しあい）でチャンピオンに返り咲いた。 (He who used to be a champion lost the position once, but got it back with the match.) So, normally it means to take up or come back his old position. 「返り咲き」is the noun. ex: 彼は社長への返り咲きをねらっている。 (He is watching for a chance to get back his position as president.) By the way, a verb with Masu-form without "~masu" is used as a noun. Not always, but often used. Ex: はなします→はなし (talk) : 彼の話は長いです。(His talk is too long.) 　行きます→行き : 東京行きの電車に乗ります。（Take a train bound for Tokyo.) I think you will be able to find another meaning of 返り咲くin your dictionary, but we rarely use it in our daily conversation. これからもがんばりましょう！