It looks like people who have bought Zclassic in order to claim their Bitcoin Private will most likely be able to do so through bittrex, bittrex have also closed widthdrawals for Zclassic.
Official Statement:
Bitcoin Private (BTCP) is a proposed "fork" of Zclassic (ZCL), combining the Unspent Transaction Output (UXTO) set of ZCL with the UXTO's of Bitcoin (BTC). The UXTO snapshots are considered the first ZCL and BTC blocks found after February 28th, 5pm UTC.
Bittrex will NOT be supporting the market for Bitcoin Private but due to issues with the Zclassic wallet, we will offer Zclassic holders on Bittrex partial support through claiming and withdrawing BTCP.
Bittrex has shut down the Zclassic wallet for deposits and withdrawals as a significant amount of coinbase transactions and UXTO's in the wallet has led to deposit and withdrawal delays. Please make sure you have cancelled any pending ZCL withdrawals. Bittrex will suspend deposits and withdrawals of ZCL until after the snapshots are complete and the wallet is in workable state.
Bittrex will suspend the Zclassic market approximately 15 minutes before the snapshot time and perform an on-exchange snapshot of ZCL balances. The market will re-open after 5pm UTC once the on-exchange snapshot is complete.
Bittrex will make all reasonable attempts to credit our ZCL users BTCP but until we have a fully supported wallet, we can not guarantee tokens. We will continue to monitor the state of the codebase and network. Since the ZCL wallet contains a significant amount of UXTO's to clean up and consolidate, we anticipate that BTCP will be available at least a week from the time of the BTCP network launch.
Bitcoin balances will NOT be credited BTCP.
Links:
https://support.bittrex.com/hc/en-us/articles/360001271272