A measurement of the speed of light with a higher degree of accuracy than the previous measurement will obtain a more precise value for the length of 1 meter.
Compare the case of the definition of the kilogram.
There is worldwide a collection of standard kilograms, and as ability to compare weights increased it became clear that the members of that collection are diverging from each other, at the microgram level.
As technology was improved a measuring instrument called Kibble balance was developed to a level where its measurements reproduced at sub-microgram level.
At that point it was deemed that the time had come to redefine the kilogram.
I don't know whether the International Bureau of Weights and Standards (located in Paris) will continue measuring the weight of the standard kilogram that was manufactured in 1889. If they do: the higher the accuracy of future Kibble balances, the higher the accuracy with which the weight of the standard kilogram will be known.