The pure maths you study at ‘A’ level is very widely applied, in fact without we would still be struggling to build bridges over anything other than a narrow river. The stuff you will have learnt at ‘A’ level is basis for all engineering, finance, fluid dynamics thermo dynamics, the world. Pretty much all science relies on maths.
More generally pure maths and Applied maths and theoretical physics feed off of each other one giving in inspiration to the other the other offering new solution to perversely unsolved problems.
Pure maths is also research in it’s own right however we never know what applications some discovers in pure maths may have. Pure maths frequently takes decades if not probably 100s of years or more to trickle down and find an application. In many way pure maths is sometimes rediscover by other but the hard work of establishing a theory and relationships has already been done.
Some pure maths may never have applications and many people who research pure maths don’t look for them when carrying out research. It all adds to our knowledge of maths which is probably the most powerful tool we have to understand the world.