I need to install a typical self-contained hot tub rated 120/240v 50amps in a detached garage. There already exists a 60amp,
3 wire service from the house that feeds a sub panel to supply an air compressor and welder as well as lighting. No power tools will be used when the hot tub is in use. My question is since the 60 amp feeder contains only 3 conductors,
can I add another #6 thwn and add a separate ground bar in the sub panel and then, feed conduit from there to the hot tub service disconnect? Or should I leave the existing sub panel alone and then run a completely new, separate conduit (with all #6THWN) from the main house panel to the garage and feed to the disconnect for the hot tub?
Note that the hot tub & disconnect will be in a separate room of the garage. The existing sub panel is in the main part of the garage.
Thanks for any help on this.

Go with the new panel. The inspector might not let you come off the existing subpanel, since you have no way to interlock the power tools with the hot tub. You would also have to get that new conductor in the same raceway as the existing, if you could.
You are better off running new.

I was under the impression that the NEC prohibits more than one service to a detatched residential garage. How about if I re-install the existing subpanel with 4 THWN copper #6, and then run conduit to the back room for the hot tub disconnect. We can disconnect the compressor & welder since the new owners have no use for them. Thanks for your help.