What is the procedure to follow for "traffic not in sight"?
Please don't use "Not in sight". Parts of radio transmissions, such as single words, can easily be cut off or missed, making it sound like you said "In sight". I commonly hear pilots use the phrase "Looking out" or something similar, which conveys a clear message: "I understood what you said, but I don't see the traffic yet".

ATC provides traffic information when there is a risk of conflict, or in the traffic circuit if we want you to follow another aircraft. No matter the reason, we will continue to update you on the traffic either until it is no longer a factor, or until you report having the traffic in sight. So, when you receive traffic information, keep looking until you see the traffic. We will keep you updated as long as it is still relevant. And please do report when you spot the traffic, that is a super helpful piece of information to us.

In the traffic circuit specifically, if you can't see the traffic being called out, you can always ask the tower to confirm you are cleared for base and final turn. When I have someone on downwind who can't spot the aircraft to follow, I will typically just tell them to continue downwind and then I will call their base turn when appropriate. But, as always, if in doubt, ask.