If a Client has an active mandate you will be able to attach this mandate to a new membership so they won't have to sign a mandate again for the new membership!
When adding a membership to a client profile (view the guide on this here), if there is an active mandate and the membership type is an auto-payments membership then an additional section will appear named 'Linked payment method'. You can select this and then any active direct debits will appear and you can select which direct debit payment you want to use for this membership. Then 'Create membership'!
If there is no set up fee (joining fee or pro rata) then the membership will be 'Active' as you have attached the active mandate.
If there is a set up fee (joining fee or pro rata) then the membership will have a 'Needs attention' status with the reason 'Set up fee unpaid'. You will have to press the three dots > 'pay set up fee' here you can then take the payment. Then once this payment has been taken, when you head back to the membership you will see it is 'Active' as the active mandate is being used!