The worm should NOT be loose...but...if it is, you can remove the slop by snugging up the collar. Don't overtighten it, it's better to have a little slop than too tight.
Although best done with the worm carrier removed, it CAN be done with it installed, just don't overtighten it.
If you have more than a couple mm of movement at the end of the counterweight shaft with the RA clamp engaged, AND this shaft DOES NOT MOVE,
then the movement is because the worm is not well meshed with the RA drive cylinder.
In that case, the worm requires adjustment.....please note that worm adjustment is, BY FAR, the usual cause of excessive RA axis movement.
Don't try to remove every bit of play in the worm/cylinder mesh. Doing so will undoubtedly result in excessively tight mesh and accelerated wear.
Did I mention you shouldn't overtighten the collar?