It’s hard to imagine that Aksel Larsen would not become the leader of the Danish People’s Republic, if for no other reason than his popularity among the general population. While I like him, I think his legacy would suffer from the thing he would do as dictator of Denmark and what he would have to do to keep USSR happy.
Outside core Denmark, I expect USA to annex Greenland and Faroe Islands and Iceland to get independence. While the Danish border would be expanded southward.
Political in Denmark I expect that the communist would establish a Socialist Unity Party like in East Germany. I also expect them to set up puppet parties, the Social Liberals or the Liberals would become the Danish Land and Peasant Party, while the other would end up the Danish Liberal Party, I don’t see a Christian Democratic Party arise instead the Conservatives and other right wingers get their puppet party; the Danish National Party or the Danish Craftsmen and Artisan Party. As in East Germany they would get some seats in parliament but all elections will be jokes.
Political I expect agriculture will be dominated by the small farmers the Social Liberals traditionally represented and which were the base of the Danish rural left. This will keep Danish society far more rural than in OTL, but dominance of small free independent farmers, will also mean that Danish agriculture won’t be completely destroyed, I also expect a focus on agricultural export for foreign capital, beside that Denmark will have a large ship and shipping industry . As result of the more rural lifestyle Denmark will keep a high birthrate for longer, likely 2,5-3 children into the early 90ties. I also expect large scale land reclamation projects to get more soil to the Danish farmers.
As for Danish industrial production outside ship building, as a communist country there will be a focus on self sufficiency. So we would likely see Danish car, bus, truck and motorbikes brands. We can guess that the brands Nimbus (motorbikes), Triangle and DAB would stay around (at least until the Cold War ends [1]. I suspect that the car production will be relative small [2] and the focus will be on mass transit, motorbikes [3], bikes and vans. A important aspect in this is their military uses, DPR need to produce these thing for military use. Denmark will also keep it weapon industry around, we will see DISA keep producing and upgrade the different Madsen guns, we will likely also see Denmark producing artillery. Denmark is a too small country for an aviation industry. Outside this the Danish weapon industry will depend on what the Soviet plan for DPR to do in case of WWIII is.
DPR will likely have one of the biggest shipping industries among the Warsaw Pact countries, this will connect have two effects. The first one will be financial. As a relative small country with a lot of people traveling the world as sailors, Danes will be aware of Western consumer products and this will force the Danish regime to produce consumer products. So we will likely see the rise of Danish electronics industry, this is pretty similar to Hungary, the different is that Hungary did it for export reasons, DPR will need to do it for domestic reason and lessen smuggling into Denmark. It will have the added benefit of electronic being prefect for a resource poor country like Denmark.
The other aspect of Danish shipping will be that DPR will be involved in a lot of Soviet proxy conflicts abroad.
At last let’s look at energy, I think DPR will focus on nuclear energy, the lack of hydro power or fossil fuel means it’s simply easier to build nuclear power plants. Of course at some point oil will be found in the North Sea and with a worse Danish-Norwegian relationship Ekofisk will belong to Denmark and with a more southern Danish border, the German oil fields also falls in Danish hands, this will give DPR a significant source of capital when it need it the most in the late 80ties and will likely soften the fall of communism.
[1]trucks, buses and motorbikes are more likely to survive the fall of communism than cars.
[2] and likely to be pretty shitty car, best case is a Cold War Fiat and worst case is a Danish Trabant.
[3] Nimbus was in OTL a work vehicle meant as a replacement for a small van, if was a way for handyman to come out to customers and it often had unique sidecars.