There is some debate as to whether or not the UK has a mandatory obligation to apply EU rules in Domestic activites beyond 2020, irrespective of what Brexit (Trade) Deal is negotiated. The Political Declaration is non-binding, but the (binding) Withdrawl Agreement says that the former must be respected using the 'best endeavours'. But there is another qualifier saying that 'the negotiating positions may evolve', and therefore surely this does not at all constrain things in any manner? Or does 'evolve' have a one-sided interpretation, i.e. evolve towards (but not away from) alignment with EU frameworks?
The UK is under no obligation to apply EU rules beyond the end of the transition period. If no deal is agreed, none of the EU treaties and laws must be upheld.
Parliament incorporated most EU law into UK law, so a change in the law would require Parliamentary approval.
The Political declaration states the intent to produce “a ambitious, wide-ranging and balanced economic partnership. This partnership will be comprehensive, encompassing a Free Trade Agreement”. But the declaration is a list of hopes and desires. It expresses intent, but doesn't bind the UK or EU to any particular set of rules after the end of the Transition period. If no deal is in place, and no extension to the transition period is agreed, then the EU and UK will trade on WTO rules, and many will judge the negotiations to have failed.
There is nothing in the Political Declaration or the Withdrawl agreement that requires the UK to apply EU rules after the end of the transition period.