Gap between bushing and tuning peg

What type of tuners are these? I don't see a nut. How is the tuner being held in place?

 

Those are a press fit bushing type, found on a majority of basses under recent American versions of Fender. Actually most Fender style tuners are built this way. That looks like a MIM in the pic.

For the OP, make sure the tuner post screw is tight and the screws aren't loose on the mounting plate on the back of the neck. Some press fit bushings have tighter tolerances than others, and honestly it's not going to make any difference in the playability as long as the post isn't binding or has other mechanical issues.

 

Never realized that and I owned a MIM jazz in the past.

 

Next time instead of glue use some Teflon plumbers tape and wrap a few times around the bushing. It will tighten up tolerances and comes off easily without any permanent damage to parts or wood