I bought a used hot tub. It comes with a 60 amp gfi switch. My home has 100 amp panel. I presently have 5 small pony boxes off the main panel. It is old style glass screw in fuses. House built in '68. Can I just add another pony box rated for 60 amp fuses ? If not, do I then need to rewire my panel with a new 200 amp panel? And if so would the existing lines from the road be sufficient or would they need to be upgraded as well?

It is almost definite that you need a complete service upgrade to 200A, not just the panel.
The line from the street is the power company's responsibility, typically everything else is yours. IE: Service entrance cables/conductors, meter pan, panel, grounding/bonding.

This is not a bad thing as it will certainly clean up the mess you likely have there now.