I do not know if I can l help as I do not know your machine.
If there is no specially made chuck then usually lathe chucks have a back plate. These can be bought usually from the lathe maker or specialist suppliers. This is a dedicated disk that has a fitting (usually a large internal thread) that matches the nose on the lathe spindle. You fit this to the lathe spindle and turn this to be true on the face and turn down a step to be the best fit you can get into a chamber in the back of the chuck. What you are doing is making a register.
You say adjustable chuck. Do you mean a four jaw independent chuck?
If so it probably has four holes that are counter-bored to take four socket head screws. (You might find these called Allen screws). The back plate is drilled and tapped to accept these. The back plate is then attached to the chuck tightening these screws firmly and then the chuck is ready for use.
Beware that centring a four jaw independent chuck may require using a Dial Test Indicator (DTI or might be called a clock or clock gauge) mounted conveniently on a magnetic stand. I have had students in tears trying to centre work. It is an easy trick to learn by adjusting two opposing jaws together to shift the work in line with the DTI half the error indicated on that jaw pair.
What you must not do is set something way off centre or out of balance and then try to start up at speed. The entire lathe will jump about violently. With a large machine it will be the last thing you do as large machines have a habit of eliminating idiots. Run slowly and increase speed until vibration starts and then run below this speed.
You can find what I mean by a four jaw chuck in Wikipedia and on the web, “fitting lathe chucks” (metalwebnews.org/mr-tools/lathe-chucks.pdf) shows an old but valid method of fitting a chuck back plate.