I am not 100% sure what happens with debit cards but as Tizme says the date will be wrong and the card number on the front will possibly change too and know with a credit card you need to update things like this.
If i was you i would log onto your online banking and ask them this very question.
edit
According to the below link it depends on how the direct debit was set up. If you set it up by giving them your bank account number you may not need to update anything.
http://q-a.moneyfacts.co.uk/446780/d...w-card-number/