Hypostasis is the Greek word for “substance”. Like the English word ‘substance’ it can have a variety of meanings, literal and figurative.
NEW TESTAMENT
For those used to older concordances linked to Strong’s numbers, G5287, here shown in KJV readings.
2 Corinthians 9:4 “Lest haply if they of Macedonia come with me, and find you unprepared, we (that we say not, ye) should be ashamed in this same confidence of boasting.”
2 Corinthians 11:7 That which I speak, I speak it not after the Lord, but as it were foolishly, in this confidence of boasting.
Hebrews 1:3 Who being the brightness of his glory, and the express image of his person and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high;
Hebrews 3:14 For we are made partakers of Christ, if we hold the beginning of our confidence stedfast unto the end
Hebrews 11:1 Now faith is the substance of things hoped for, the evidence of things not seen.
It is perhaps Hebrews 1:3 that is the starting point for later Trinitarian theology using hypostasis to speak of God’s person and Christ’s person, and therefore of hypostatic union, union of the substances or persons. Obviously this idea is not present in the New Testament.
SEPTUAGINT
The Greek translation of the Old Testament contains 19 uses:
Deu 1:12 How can I myself alone bear your cumbrance, and your burden, and your strife?
Deu 11:6 And what he did unto Dathan and Abiram, the sons of Eliab, the son of Reuben: how the earth opened her mouth, and swallowed them up, and their households, and their tents, and all the substance that was in their possession, in the midst of all Israel:
Jdg 6:4 And they encamped against them, and destroyed the increase of the earth, till thou come unto Gaza, and left no sustenance for Israel, neither sheep, nor ox, nor ass.
Rth 1:12 Turn again, my daughters, go your way; for I am too old to have an husband. If I should say, I have hope, if I should have an husband also to night, and should also bear sons;
1Sa 13:21 Yet they had a file for the mattocks, and for the coulters, and for the forks, and for the axes, and to sharpen the goads.
1Sa 13:23 And the garrison of the Philistines went out to the passage of Michmash.
1Sa 14:4 And between the passages, by which Jonathan sought to go over unto the Philistines’ garrison, there was a sharp rock on the one side, and a sharp rock on the other side: and the name of the one was Bozez, and the name of the other Seneh.
Job 22:20 Whereas our substance is not cut down, but the remnant of them the fire consumeth.
Psa 39:5 Behold, thou hast made my days as an handbreadth; and mine age is as nothing before thee: verily every man at his best state is altogether vanity. Selah.
Psa 39:7 And now, Lord, what wait I for? my hope is in thee.
Psa 69:2 I sink in deep mire, where there is no standing: I am come into deep waters, where the floods overflow me.
Psa 89:47 Remember how short my time is: wherefore hast thou made all men in vain?
Psa 139:15 My substance was not hid from thee, when I was made in secret, and curiously wrought in the lowest parts of the earth.
Jer 10:17 Gather up thy wares out of the land, O inhabitant of the fortress.
Jer 23:22 But if they had stood in my counsel, and had caused my people to hear my words, then they should have turned them from their evil way, and from the evil of their doings.
Eze 19:5 Now when she saw that she had waited, and her hope was lost, then she took another of her whelps, and made him a young lion.
Eze 26:11 With the hoofs of his horses shall he tread down all thy streets: he shall slay thy people by the sword, and thy strong garrisons shall go down to the ground.
Eze 43:11 And if they be ashamed of all that they have done, shew them the form of the house, and the fashion thereof, and the goings out thereof, and the comings in thereof, and all the forms thereof, and all the ordinances thereof, and all the forms thereof, and all the laws thereof: and write it in their sight, that they may keep the whole form thereof, and all the ordinances thereof, and do them.
Nah 2:7 And Huzzab shall be led away captive, she shall be brought up, and her maids shall lead her as with the voice of doves, tabering upon their breasts.
These are broadly in line with the uses you would expect in classical Greek.
CLASSICAL GREEK
The full entry from Liddell Scott for hypostasis is as follows.
ὑπόστα^σις , εως, ἡ, (ὑφίστημι, ὑφίσταμαι):