You could click on the column header to sort them so that any new notes appear at the top of the list.
I don't think it is possible to filter on that 'column' unfortunately.
The closest i can come to it is to set up a Search query that will show currently Open tickets that were updated today (or in last X minutes/hours) AND have (at some point) had a client note added to them. The drawback is that it only really filters on "some update was made today" but it doesn't necessarily mean that the Client Note was added today...just that some Client Note was added since the ticket was opened. So the "history contains 'added new client note' piece only serves to filter out the tickets that haven't ever been updated by the Client.
if you were to create such a query then you can just run it whenever you'd like from any 'normal' ticket view by going up to "Query" and selecting it.