Adding a hot tub which needs a 220 60 amp circuit
Assuming that the wires are appropriate for 60 amps (6awg copper is rated for 55 amps at 60c and I believe you are allowed to “round up” to the next higher breaker size, 60 amps) then yes, you can simply replace the old dual 30 amp breaker with a dual 60. (Cap off or remove the old wires running to the 30.)

Note that a hot tub requires GFCI protection. This can be done by using a 60 amp GFCI breaker in your panel or by using a GFCI cutoff switch near the hot tub.