To ensure that your journeys count towards the capping, the same card needs to be used. For capping, the same card does need to be used through the period.
Since your replacement debit card will have a different card PAN number, it is encouraged that you register on TfL and update your PAN number so that they recognise your new card and you can continue to track and view your journey history online. It is also advised that you start using your new card on a new week to benefit from Monday to Sunday capping. Please remember that a Chip and PIN transaction needs to be completed to activate Contactless usage.