Your Core Purpose is eternal because you are eternal.
That which you are intrinsically great at, that which is hard-wired into you, will not die, because your Core Competence is between your ears, and is expressed with your mouth, your hands,  (Ecc 9:10) your feet, your back etc.  But these are just the means by which your Core Competence is expressed.   Your Core Passion is that chief concern, outcome or achievement or “effect”, that when you experience it resonates deeply within your heart. And this Passion is also give by the Eternal God.

Your Core Purpose is the product of your Core Competence [see footnote] , which is directly “hard-wired” into you,  pointed at, what you really care about- your Core Passion– (which is given from God in Psalm 37:4-6),  Since your Core Purpose or what I have also called your “Life’s Work”, and since your Life continues after your body dies, your Core Purpose goes with you.

So this Core Purpose continues on into the eternal life you have.

Here is some Biblical proof-   In John 10:10 and in Luke 4 Jesus proclaims both his Core Purpose and his Vision for Humanity.  In John 10:10 Jesus says He has come to give us LIFE, and that…to the full!  A full life.  THIS is his core purpose.  This is full alignment with our eternal purpose in John 17:3,  eternal life comes from “knowing” God and Jesus Christ whom he sent.

So is Jesus Core Purpose finished?  By no means.  He is now to this day at work bringing us this Life this full and satisfying Life he proclaimed in John 10:10.  ( The Enemy’s Core Purpose is also identified in that same passage in John.)

Jesus also had a mission– and a mission is NOT eternal and therefore is NOT a Core Purpose.  Jesus’ mission is proclaimed in Matthew and other places in Gospels.  But note, that this mission has a beginning, with his baptism by John, and an end, on the Cross.

In Matthew 20:18,19

18 “We are going up to Jerusalem, and the Son of Man will be betrayed to the chief priests and the teachers of the law. They will condemn him to death 19 and will turn him over to the Gentiles to be mocked and flogged and crucified. On the third day he will be raised to life!”

The Holy Bible : New International Version. 1996, c1984 (electronic ed.) (Mt 20:18-19). Grand Rapids: Zondervan.
Jesus can only sacrifice himself on the cross ONCE!.  And he did.  And just before he died he proclaimed the words that prove the point and achievement-  “IT IS FINISHED”.    Mission Accomplished.  But his Core Purpose continues, eternally, to give us a FULL and SATISFYING LIFE!
There is a question here-  If Jesus’ Core Purpose is eternal, is ours?  If my understanding of it is correct, then it continues with you, for eternity, because you will still be you.
love to read your comments……

Footnote on Core Competence- Since we will be judged according to what we have DONE, it is reasonable that that what we are asked to DO by God, we are also capable of doing!

Ps 62:12 and that you, O Lord, are loving. Surely you will reward eachpersonaccording to what he has done.
Prov 24:12 If you say, “But we knew nothing about this,” does not he who weighs the heart perceive it? Does not he who guards your life know it? Will he not repay eachperson according to what he has done?
Matt 16:27 For the Son of Man is going to come in his Father’s glory with his angels, and then he will reward eachperson according to what he has done.
Rom 2:6 God “will give to eachperson according to what he has done.”
Rev 20:13 The sea gave up the dead that were in it, and death and Hades gave up the dead that were in them, and eachperson was judged according to what he had done.
Thanks for advancing God’s Work in Progress