Enkainizo means to make new, to inaugurate, to dedicate, or to renew. It appears twice in the New Testament, both in Hebrews: once referring to Moses' inauguration of the first covenant with blood (Hebrews 9:18) and once to Christ's inaugurating a new and living way by His blood (Hebrews 10:20).
The use of enkainizo in Hebrews draws a direct parallel and contrast between the old and new covenants. Moses inaugurated the Sinai covenant with the blood of animals (Hebrews 9:18-20); Christ inaugurated the new covenant with His own blood (Hebrews 10:20). This is not mere renewal but a fresh, superior dedication — the inauguration of a 'new and living way' through the tearing of the veil, symbolizing Jesus' flesh. Every time believers approach God in prayer, they walk the path that was enkainized — freshly opened and dedicated — by Christ's sacrifice.