In most cases its possible to replace your existing bulb with a smart light, however you will need to check that the smart light is available in the same fitting your current bulb uses. Most smart lights come in screw or bayonet fitting, while some brands also offer GU10s and Candle Bulbs.
In some cases, smart light bulbs are bulkier that standard bulbs, for example the LIFX A19/A60 bulb, which may mean in some cases it protrudes from  your existing lamp or shade - a look, which you may not be happy with. So always check the dimensions of the smart light against your existing bulb.
It's also important to remember, that once you swap out an existing bulb for a smart light and pair it with the relevant app, you'll need to use the app or a voice assistant to turn it on and off. If you use the light's own switch, once its turned off, it can no longer be controlled by the app or compatible voice assistant.