As others have said, the likelyhood is that the vaccine will stop or reduce transmission. We simply don't know yet.
It would be rare for a vaccine not to do so, but there are examples of this. The reason for this is that our immune system is really a series of interlocking systems. There are innate systems - our skin and stomach acids, and immune cells that attack anything that looks alien. And adaptive systems, which learn how to respond to threats, and which are what vaccines trigger. But the adaptive system in itself divides down into compartments. The mucosal immune system (the system in the linings of the mouth, nose and gut) in particular is slightly seperate from the central system.
Which compartment you trigger depends on where you get an immune response. If the vaccine (or disease) is swallowed, you get good immunity in the bowels. If it's squirted up the nose, you get good immunity in the nose, throat and lungs. If you inject it, you get good internal immunity.
There is some overlap between the chunks of the immune system, but an exposure to one section of the immune system won't necessarily trigger much of a response in the others. In particular, injected vaccines don't tend to trigger much of a response in the mucosal or gut immune systems.
This is why the inactivated polio vaccine doesn't stop transmission. Polio is mostly a disease which lives in the gut - it transmits when the faeces of an infected person contaminates the food or water that someone else drinks or eats. And it does no great harm there. People get ill with polio when the organism leaves their gut and invades their nervous system. The inactivated polio vaccine is an injection, which creates an immune response carried by the blood. Those defences are triggered when the organism tries to spread into someone from their gut. It works really well to stops people from getting sick. But it doesn't attack the organism when it is living in the gut, so it doesn't stop people from carrying or transmitting the virus. The oral polio vaccine, on the other hand, is swallowed and creates a good immune response in the gut and so does stop the disease from spreading.
Covid enters the body and lives in the linings of the nose and throat. You only get really ill if it enters into your body from there. We know the vaccine is really good at stopping that. But the nose linings are mucosal immunity - a different system - and we don't yet know to what extent the covid vaccine injection will trigger immunity there. The virus may continue to reproduce in and spread from the nose/throat. The likelyhood is it will reduce the amount of virus hanging around in the nose and being coughed or sneezed out, and so will reduce spread, but this remains an unknown.
As with everything, more research needed.
(And as with everything I'm open to criticism/correction from the people who understand this stuff much better than I.)