Sometimes. Heat pumps deliver water at lower temperatures than a gas boiler, typically 45 to 55 degrees rather than 70 to 80. If your existing radiators are generously sized, they may cope. If they are small, they will struggle to get the building warm enough, and you will need to upsize some or all of them.
A heating engineer can calculate the heat loss of your building and compare it with the output of your current radiators at heat pump flow temperatures. That calculation tells you whether the existing system will work or whether you need larger radiators, fan convectors, or a hybrid approach.
The pipework itself can usually stay, which saves a significant amount of disruption and cost compared with a completely new wet system.