How will space be used for military purposes in the future?

It already is being used for military purposes right now as in spy satellites. Even very recently SpaceX was tasked to launch a U.S. spy satellite into orbit but it exploded and the satellite didn’t make it.

In 1984 a Titan 34D rocket launched the KH-9 and KH-11 satellites for “reconnaissance,” and the DSP-2-6R satellite for missile detection. The list just starts there and goes into the hundreds including many intelligence-gathering satellites and so on.

And, by the way, not just by the United States, but other governments as well.

Furthermore, the Chinese government once shot a missile to destroy their own satellite in space just to say the could, and they succeeded, vastly increasing the dangerous debris cloud floating now in orbit. It was a military demonstration.

Edit addendum: The government of India has recently done the same foolish thing – shot down a satellite to prove they could do it – increasing the amount of space junk exponentially.