i dont quite understand how long the top has been leafless .... but if its been for an entire growing cycle.. then the top is dead.. and should be removed .. if for no other reason than its ugly .. and dead ...

since your new shoots look rather tender.. i might not go as far down as your red line.. just for fear of breaking them off ... no one says you have to make one cut ... do it in stages ...

the fact that your new shoots are not growing straight up.. like a tree.. indicates to me.. that it is not getting sufficient light ... but if you repot it.. dont slam it into more light immediately ... let it recover from the stress of repotting .. before you stress it again ...

of course.. once you remove the top.. you shouldnt need the stake ...

ken

I am not convinced this plant will ever be tree-like again....sorry :-( Yes, I'd cut off the dead top but I think the best you can hope for is a low growing shrubby specimen (although Al might suggest converting this into a bonsai :-)).

Honestly, unless you are inclined to a lot of pampering of a not very happy plant that may never look very good, I'd just toss it. Olives are difficult at best to grow as a houseplant and it is hard to get it enough light indoors for it to do well.

To figure out if the top is dead or not: Start clipping from top down may be an inch or so at a time. Check the cut portion still attached to the main stem. You should see a faint green ring just under the the bark and the inner core should be whitish. If it is dead at that location then you would not see the green outer ring and the core would be brownish. Work your way down the plant and at some point you should see live tissue. Maybe pretty close to the tri-furcation. But at least you can rule out whether there is any living tissue in the main stem beyond the living sprouts.

It is quite likely the main stem is dead and the cut location you marked is pretty good.

Olives like to be on the dry side. In winter, cool dry condition is not only OK but desirable for olives. But they do need to be in bright location. Bright like on a southern exposed window. The location you have does not look like bright enough.

The top might still be alive I would cut it centimeter by centimeter to find out. Cutting the tree will not help it in any way right now. The problem seems to be it had a lack of energy and the foliage wasn't able to be sustained up top.
Make sure the pot drains well when you water it so no perched water stays at the bottom of the pot (maybe half of your root system is rotted right now).
Give the tree some good light, so behind a window or installing a grow light. These leaves at the bottom seem to be the tree's last ditch effort to survive. Feed them light as soon as possible.
I would not advise repotting the tree right now because that will stress the roots and may further hurt the tree's health. Later on if it has survived and shows growth, you can pot it into a good soil, like you were talking about.

Now that I look at your picture I see a ring of white deposits around the inside of the pot and around the trunk. Was the pot not able to evacuate water for a while? My first plant died like this.

Thanks all for your help! I will change the soil this weekend!