Nope.
For user security, once a Privacy Card is closed, it cannot be re-opened. Any transactions in progress, as well as current or future refunds, will be processed without any issue. A new Privacy Card will need to be created if another purchase is necessary with this merchant.
If you anticipate needing to use a Privacy Card more than once with any one merchant, we recommend creating a Merchant Card and pausing it, rather than closing it. Cards can be paused and unpaused at any time and no new transactions can be authorized on a Privacy Card while it's paused.