Ive got a young ligustrum mallsai as a present so Id like to put it into ground in my garden for long years. It should be done early spring as well as general repottings?
Soil is terrible. Too small. Drains well but its only because there are roots outside of the soil everywhere.

Probably not if you live in Finland and it is a ligustrum japonica.

Chinese privet it is and I live in central europe(hungary)

If you want to plant it in the ground thats ok, and yes, do it in spring.
But if I understnd you, you think that the soil is terrible because the roots are comming out of the pot. If they are comming out at the botom it might be because the tray is often full of water and they are following it. You can just cut these or transplant in a bigger pot without pruning the roots. Usually when the soil is really full of roots the soil doesnt drain so well as it used to, so Im not sure your soil is bad.
But yes, panting in the ground is even better to grow the trunk.

Depending on the variety, this species can tolerate frost of a few degrees to in some cases up to -15. Verify whether this is a hardy type or not.

If you just want to take it out of the container, you can do that now. If you want to do some rootwork, which I would recommend, do this in spring.

I don't know if I can wait until spring. It is outside in half shade. I water it everytime the soil gets slightly dry but not stone dry. It still loses leaves and most of them started to turn yellow. I also think it is root bound.

Madartej21 wrote: I don't know if I can wait until spring.

Why don't you give waiting a try? You might like it.

Maybe because I dont want it to die. It keeps losing and deforming leaves even though it gets proper care (at least as proper as a mallsai can get)