There are only five occurrences in the NT, in general used in the sense of assurance, substance, reality. Definition (lit: an underlying): (a) confidence, assurance, (b) a giving substance (or reality) to, or a guaranteeing, (c) substance, reality. The occurrences are: 2 Corinthians 9:4 – ἐν τῇ ὑποστάσει ταύτῃ (by this confidence); 2 Corinthians 11:17 – ταύτῃ τῇ ὑποστάσει τῆς καυχήσεως (in this confidence of boasting); Hebrews 1:3 –χαρακτὴρ τῆς ὑποστάσεως αὐτοῦ φέρων (and the exact representation of His nature, and upholds); Hebrews 3:14 –ἀρχὴν τῆς ὑποστάσεως μέχρι τέλους (the beginning of our assurance firm); and Hebrews 11:1 – πίστις ἐλπιζομένων ὑπόστασις πραγμάτων ἔλεγχος (faith is the assurance of [things] hoped). See: http://biblehub.com/str/greek/5287.htm
