Shared ground
These lines function as a closing spoken blessing. The writer asks God to supply what the audience lacks so they can carry out God’s will (explicit: God “make you complete…working in you”).
God is identified in ways that gather up major themes from Hebrews: God is “the God of peace” (explicit), God raised Jesus from the dead (explicit), and Jesus is “the great shepherd of the sheep” (explicit). The blessing treats Jesus’ death (“blood”) and an “eternal covenant” as the basis for confident hope and ongoing moral formation (explicit that the terms are linked; inferred that this is the ground of the request).
The goal is not only outward behavior (“every good work”) but also an inner reshaping (“working in you what is well pleasing in his sight”), and this happens “through Jesus Christ” (explicit).
Where interpretation differs
1) What “with/by the blood of an eternal covenant” most directly connects to.
Some read it as saying the resurrection happened “by means of” Jesus’ covenant blood (so the blood is tied to how God raised him). Others read it as a compressed phrase tying Jesus’ identity as shepherd—and God’s saving work more broadly—to the covenant established through his death, without making the blood the means of resurrection.
2) Who receives the closing “to whom be the glory.”
Some take “to whom” as referring to Jesus Christ, since he is the closest mentioned person (“through Jesus Christ, to whom…”). Others take it as referring back to God, since God is the one doing the equipping and inner work, and the blessing began by addressing God.
Why the disagreement exists
The Greek wording allows more than one way to attach the phrase about “blood…covenant” to the surrounding verbs and titles, and the final pronoun (“to whom”) could grammatically point to either God or Jesus.
What this passage clearly contributes
It portrays God as the active agent of believers’ moral and spiritual formation (explicit: God “works in you”). It holds together Jesus’ resurrection, his caring leadership over God’s people (“shepherd”), and the covenant made through his sacrificial death (explicit links). It also frames endurance and obedience as something God equips and produces, not merely something the community must generate on its own (inference drawn from the repeated divine action language).