Most likely you will need a qualified gunsmith to diagnose and repair it. For a gun like this, it could be cost prohibitive.
Is the play apparent in the had or could it just be the cylinder stop (the thing that is under the cylinder and sets it into place. Often the "Star" looks worn but isn't to the point of failure.
Has the weapon ever had a "trigger job" or an "action job"?
To check basic functionality, you can unload the weapon and then close the cylinder, take up the slack in the trigger and then start the trigger pull, but hold it so it doesn't release. Look at the cylinder stop as you attempt to rotate the barrel to see if the play still exists. If it does, then the "lockup" issue is likely to have more to do with the stop than with the ejector/"star".
Look at the face of the frame to see if the hand (the little beak looking piece that moves out of the frame as the hammer is drawn back) is very altered, deformed or broken at the tip. If this is the case, then it is likely that the hand is the cause of the timing concern.
That said, any further diagnosis would likely be better performed by a gunsmith in person, and an estimate made then to the cause/cost to repair. other causes can be weak springs, believe it or not, or an unbalanced crane, both of which are not easily repaired in conjunction with parts fitting (though anyone who can strip their revolver can re-spring it) and tuning the gun to the springs