In Traveller it seems like thousands of years go by without much in the way of major scientific discoveries. IRL, advancement has just gotten faster and faster over the past 500 years; 500 year ago, a person might die of old age in basically the same kind of life they were born to, but by 200 years ago this was no longer true, and today this level of change is compressed in to single digit years. A 20 year olds' life these days is dominated and structured by the capabilities of smart phones, 10 years ago these were new, and 20 years go they basically didn't exist. Over the next few years, the development of AI is probably going to make allot of the futuretech in Traveller look kind of silly retro. Traveller assumes a kind of slow advance over the centuries, with some worlds going forward, and others regressing, and the slowness of travel basically meaning they do this independently. I find this kind of unlikely, but I guess it might happen this way, given this speed of travel in the game and it works for the setting.
I assume that TL level is really about the tech that is available for purchase on a world (either manufactured, or imported), and does not mean that the world has that level of science. The tech and science are related but not exactly the same. The major scientific developments: i.e. understandings of how the universe works, are not going to be fenced off by TL. If you want to read a research article which is pushing the frontiers of basic physics, it is going to be available as soon as the news of its publication reaches your world. We can assume that information flow is not very good in low tech societies and probably those that have mid-tech levels might not be as plugged in.
To do cutting edge science, it helps to have the highest possible tech, but it isn't the only thing. And how much it helps depends on which science, and what kind of research question you are tackling. A low tech world could still have biologists publishing important new discoveries about the life forms on their planet, but discoveries in genetic engineering will depend more on lab tech. If you want to push the frontiers of physics, you'll probably need Tech 15 or 16 equipment.