Depends on the type of star and why it lost part if it's arm. Most stars can regenerate if the water quality good and availability of food is enough. If the star is suffering from a disease or being eaten you will have to eliminate the problem first then with good quality food and water it will be fine. A few ot the short armed stars can't fully regenerate, but will live a full life with a piece missing if the wound heals.
Good luck, and find out why the part of the arm is missing and you can then take care of it.