It would be technically very difficult to do this. When you search for a client (or any other sort of textual search) it runs a query against a very large dataset that compares the partial search with the client names. If they were in an encrypted state the server would need to first decrypt millions of records before the query can be fulfilled. The performance overhead involved would be huge. With predictive searches it's actually running a query with every key-press.
The best practice when it comes to securing data is to hash sensitive credentials like credit card numbers and passwords. We don't hold any credit card details on our servers but we do hash all passwords we store.
From what I know the Talk Talk hack was due to a simple SQL Injection, this is a vulnerability that has been around for over a decade. It is very well documented and easy to protect against.