In 1 Peter believers are represented as a Priesthood that 'offer spiritual sacrifices'. Assuming that they can't be for expiation as only Christ was worthy to offer his own soul for that (represented by animal blood in the OT) what sort of sacrifices are these?:
As you come to him, a living stone rejected by men but in the sight of God chosen and precious, you yourselves like living stones are being built up as a spiritual house, to be a holy priesthood, to offer spiritual sacrifices acceptable to God through Jesus Christ. (ESV, 1 Peter 2:4-5)
Note: I used a technical word that seems to require a definition.
Guilt is said to be expiated when it is visited with punishment falling on a substitute. Expiation is made for our sins when they are punished not in ourselves but in another who consents to stand in our room. It is that by which reconciliation is effected. Sin is thus said to be "covered" by vicarious satisfaction. The cover or lid of the ark is termed in the LXX. hilasterion, that which covered or shut out the claims and demands of the law against the sins of God's people, whereby he became "propitious" to them. The idea of vicarious expiation runs through the whole Old Testament system of sacrifices. (Bible Dictionary)