This is obviously rather vague, but a post here suggests the budget is '£150m-250m', which is quite substantial. Possibilities include:comprehensive upgrade to improve traffic conditions on the main link between the Port of Liverpool and the motorway network. This scheme was identified as a central element of the Liverpool Local Growth Deal.
1. Improvements to the entrance of the Port itself. If we literally understand the improvements as being to Princess Way itself, that is only a very short section of road from the Port entrance to the Bridge Road roundabout. To spend that kind of money here, the plan would presumably be something like grade separating the Bridge Rd roundabout and further grade separation of the A565 junction. The current junction puts the A5036 into a roundabout under the A565. Port Access would be improved if the A5036 instead freeflowed into the Port, for instance, via a stackabout. This would, however, seem like overkill given how poor the rest of the connections from the motorway are, so this is unlikely to be what's planned.
2. Improvements to the entire A5036. On a broader reading of 'A5036 Princess Way - access to Port of Liverpool', the entire A5036 would be improved. There is a large number of at-grade junctions, and even if only the major junction are grade separated, with others LILOed, it's easy to see £150m-£250m being spent along the road. Even so, this would require quite a lot of demolition, so we might have doubts about whether that is really the plan.
3. Improvements to the A5036 and to Switch Island. Most tantalisingly of all for sabristi, the plan may be to improve the infamous M57/M58/A5036 Switch Island junction as well as the A5036. £150m-£250m would be sufficient to carry the A5036 over or under the junction as a continuation of the M57 or M58 mainline. Since much of the budget would be spent at Switch Island in this scenario, improvements to the A5036 would be smaller scale and involve less demolition.
Of these, it seems to me that no. 3 is most likely. Thoughts?
PS - There are two smaller schemes in the area presently under construction - see here and here. The first of these is part of the 'Pinch Point Programme', and like much of that programme, is likely to be demolished if the more ambitious plans recently announced go ahead...