flat concrete roof with weathering course leaking in many places
A new layer of waterproof material; generally referred to (here) as a re-roof , though of course you would not be replacing the concrete roof. Depending exactly what you mean by a "weathering course" that will probably be getting replaced, removed and replaced on top of a new waterproof membrane located under it, or covered by the new roof system.

Re-roofing is generally the best/most economical time to consider whether you might benefit from adding insulation to your roof to mitigate heat and/or cold passing through it.