You have to set the end date of the old operation and create a new operation with the next day as it's start date. If you give the new operation the same operation number you don't have to modify the component, but if you give the new operation a different operation number you have to make a similar change to the BOM. In this case you would set the end date for the component linked to the old operation and create a new component record linked to the new operation and its start date the same as the start date assigned to the new operation.  

Each record on the product structure has a unique key  parent/comp/ref/start date.  If any of these 4 fields are different it will create a new record.  So you will need to do 2 steps.
1.  go into the existing record and in the second frame set the end date
2. add a new record with same parent/part/ref but with a start date as the day after whatever you set the end date to on the first record but set the operation to the new operation number.

NOTE.  If you then decide that you need to change this then you will need to do the following because you cannot just type in a different start date as that would create another record.
1.  Go into the original record and in the second frame adjust the end date to show the new date.
2. Go into the second record you created using the original new start date and then go to the start date field on the second frame and chage it there.  This will actually change the key to the record so that in future it will have the new start date as the key.

ALSO please remember that an WO, Prodction Order or schedule, will still be picking up on the original product structure if the wo has a status of E, A or R as thay already have their own BOM.  If it is P or F it will be ok as it will pick up the new BOm when it is released.  For schedules you will need to close the existing one so a new one can start