If the nearest star is 4 light years away, does this mean its light will reach us after 4 years?

"If the nearest star other than the sun is 4 light-years away, does it mean [its light] will reach us only after 4 years?" - Question posed by Marcus

Yes.

A 'light year' is the distance covered by light in one year (more here), so four light years would be the distance travelled by light in four years. This definition means that any light emitted by something four light years away from us would take four years to get here.

The nearest star to Earth that isn't the Sun is Proxima Centauri. It is a red dwarf star, a bit more than four light years away. It can be seen in the constellation of Centaurus and was discovered in 1915 by Robert Inns.
Proxima Centauri is smaller than the Sun, having about one eighth of the mass and one seventh the diameter. It therefore has a lower average luminosity and will live a lot longer than the Sun.

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