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Clean out the crack. Paint the raw edges of the exposed plaster with a bonding agent like PlasterWeld by Larsen's Products. There are other brands. Use a setting type of joint compound. It is more compatible with plaster than ordinary joint compound. Fill the crack flush and sand it smooth. It may take two coats. You can give it a second coat as soon as the first one sets. Let it dry before you sand it. There is some chance it will still crack. You will have some more success if at this point you tape over it with paper tape and joint compound. It might let it move beneath the tape and not show the crack through the surface.
One other thing to look for is to see if the plaster key has failed at the crack. The plaster will be pulling away from the wood lath. Some gentle upwards pressure and some drywall screws should take care of it. Ditto John's comments on the use of setting type joint compound.