You can't drag a nested option to a different parent option. Instead, you create the option again under the new parent and replace the old one. This keeps the values on existing tickets.
Before you start
save a list of tickets that use the old option, so you have a backup. You can do this with a DPQL report:
SELECT tickets.id, tickets.custom_data[#]
FROM tickets
WHERE tickets.custom_data[#] = 'field_value'
ORDER BY tickets.id ASC
Replace # with the field ID and field_value with the option you are replacing.
Move the option
Go to Admin > Ticket Structure > Ticket Fields and open the field.
Create a new nested option with the same name under the correct parent option.
Click Save.
Delete the original option and choose Delete and replace with.
Select the new option you created.
Click Delete.
Existing tickets now show the new option.
Troubleshooting
The option didn't change? Make sure you clicked Delete, not Keep. Keep cancels the deletion.