Costs are going down for space technology, and needful infrastructure is available at more and more places in the world. The space race of the 60s was motivated by propaganda stunts in a polarized world.

For today there are two major drivers: establish a foothold for humanity on a diffrent world in case earth becomes ecologically uninhabitable, or to start developing space comercially.
For commercial delvelopment most governments see that a basic infrastructure needs to be put in place. For US, this is not so much a government problem as NASA has already made (and are making) investements in tech and infra so private enterprise already could start (read SpaceX).
Other governments are investing not to be left behind in the coming space exploitation.

So yes - there is a new space race coming, but the drivers are governments and big enterprise. as time goes along smaller enterprise will become more prominent.

Before creating place for humans in space, you should have started with saying new ERA of Space War. US, China, Russia were having Anti-satellite weapons (ASAT) which are space weapons designed to incapacitate or destroy satellites for strategic military purposes and now India has joined them and rest will follow. How will we stop that, which is creating hell lot of destruction in Space, recently we heard that the debris out of these tests are going to be dangerous for ISS ( International Space Station). How about this?

The commercial development of the moon will start once costs of getting there fall. Elon Musk's rocket system has shown technology exists to get there (and importantly) get back. I expect to be able to call uber to get me to the moon in 10 years.

Maybe a new space race could start but new players are involved now. Indeed new technologies are developed but to have these extended to consumers, these must be scalable.