For instance, after having taken a capital city, how would the postal or taxation services of the conquered kingdom be brought under control?
I am specifically interested in classical antiquity, but I'm sure there are other good examples outside the time period (The Norman and Mongol invasions come to mind).
There were no postal services in antiquity. In fact, there were little to no government services at all. The government mostly provided protection, justice, and obeisance to the gods. In return the government demanded money for taxation.
Rome, for example, had multiple options for how to fulfill those services in conquered territory. Most of the time Rome would allow conquered peoples to govern themselves in return for tribute. In order to understand the thought process, it's best to start with the process of conquest.
Romans had many levels of surrender. The most dire was the deditio in fidem, unconditional surrender. A city was forced to drag the gods out of their temples and set them before the Roman commander along with all their wealth and property (this was often done symbolically). The Roman commander would then return the gods and take whatever property they wanted. This essentially means that Rome fulfilled the obligations of a ruler by maintaining religion and giving justice (theoretically the army was dispensing justice in the first place).
After surrendering, Rome provided arbitration in the form of a traveling governor (like a consul or promagistrate if the town was in a province) or by allowing audience in the Senate. And defense in the form of its army.
Most of the time, Rome wanted conquered cities to see after themselves and thus allowed local government to continue as it was. They could promote support by giving favor to supportive local elites or by maintaining a military presence. If a region was not urban enough to do this (the Ebro valley of Spain comes to mind), Rome would establish cities called municipia which had governments modeled on Rome itself and settle the locals in them. The religion and justice system would also be modeled on Rome. In return they offered Roman citizenship to magistrates in municipia.
Taxation was gathered by private contractors called publicani. They were a major influence in Roman imperialism just like military contractors today! They would give the Senate a guarantee of the tax revenue for a region and have the support of the Roman governor (magistrate/promagistrate) to collect it. They pocketed any extra, encouraging them to be rapacious but also low-ball the Senate (hence the distaste for tax-collectors in the New Testament).
Augustus and Agrippa made the system much more regimented by placing cities in a hierarchy in order to weaken the publicani, but they still relied on local cooperation for collecting taxes.