If you bought your tickets directly with Turkish, then things should be clear
Presentation of Credit Card: If our system detects risks regarding the transaction, you will need to present your credit card for the tickets purchased via our web site and mobil application before the flight. The system asks for your approval concerning the presentation of your credit card if risks are detected regarding the transaction. (“You will be requested to present your credit card before the flight. Do you approve of this request?”).
Situations That Do Not Require Presentation of Credit Card: If you did not encounter any prompts regarding the presentation of your credit card during your transaction, you will not be requested to present your credit card. This procedure will also not be necessary for tickets purchased with 3D Secure approval.
Also have a look here regarding this.
If however you bought your tickets through a third party (say expedia), then I don't know how this is being handled. There are reports of denied boarding for failure to present the card.
Turkish does mention the CC requirement for Online-Checkin
Passenger who paid the ticket by credit card should keep their ID and also the related credit card to show it out to the boarding agent.
while no such thing is mentioned for checking in at the counter - however that means nothing given the above.
To be on the safe side, see if you can obtain a copy of the old card, a statement from the bank or anything that proves you have been the rightful holder of said card. Also your new card might have the same number and be useful. If you want to make even more sure, contact TK customer service, e.g. via twitter and ask if you can give them your booking number to check whether the CC is required.