There are three main ways to improve you lap times. Brake LATER and later, go faster in FAST corners and FOLLOW the leader.
Firstly it is in-built survival to not go too fast too soon and as it should be. No point being a “hero” only to crash out early. Slowly leave your braking later and later as long as you feel comfortable.
Even when you are gaining experience a lot of riders will tell you they are braking at say the 100 metre-braking marker when you can see they are rolling off at about 120 metres. This is the gap between slowing down and actually applying the brakes. Problem is someone will go past you flat out whilst you are easing up.
The trick is to get this gap as small as possible – to transition from rolling off to applying the brakes should be simultaneous. Try leaving your braking a little bit later each lap. Find a corner you are having a particular problem with and go another meter or two deeper each lap. Make sure there is an escape route – somewhere you can run off if you do not make it.
To learn how to brake better refer to the book chapter on Braking plus the section on trail braking.
Again at both tracks the corners leading onto the straight will determine your terminal velocity down the long straights. If you enter the straight 10km/h faster then the next rider on the same bike you could be going 20km/h faster by the end. How much more power would you need to go that much faster? I will let you work that out.
Most crashes occur on the slowest corners because it is easy to ride nearer the limit without the skills to do so. It is much harder to ride near the limit when the speed intimidates you. This is just as well because of the consequences of crashing at high speed.
Make sure the person you are following is very experienced. No point in learning from someone who is fast but only because they are over their limit and they know little more than you.
They should be faster but not be going 10 seconds a lap faster. Quickest way to ride beyond your limits and crash is to try and hang on to someone too fast for your ability.
Best is to go to “school” and have an expert both lead and follow you. That way they can see ways to improve your riding, not just trying to work it out for yourself. But note not all schools are created equal... look around to find one best for you.