Check out the lifecycle prefix https://wiki.openstreetmap.org/wiki/Lifecycle_prefix. In a case like this it could be tagged as

construction:highway=motorway|trunk|primary|whatever

An alternative would be to use the highway=construction tag https://wiki.openstreetmap.org/wiki/Key:construction#Highways. In which case the tagging would be something like:

highway=construction
construction=motorway|trunk|primary|whatever

Since the two tagging methods don’t conflict, you could even use both:

construction=motorway|trunk|primary|whatever
construction:highway=motorway|trunk|primary|whatever
highway=construction

I am not sure if any data users (renderers, routing, navigation apps) use any of the above so it probably doesn’t make much difference which tagging you use. It is mostly information for the next mapper to come along, especially after the construction is complete.