What would happen if a 13a fuse is put in a tv?
Nothing until the tv develops a fault, then it might catch fire and set your house alight. The correct value of fuse should always be used.
A fuse is a circuit safety device. Asking this question must mean that the fuse has blown. It has blown for a reason. The reason has to be found before a new fuse is installed. If the reason has been found and corrected then the fuse that the manufacturer recommended should be re installed. It is your option to use a larger fuse that what is recommended. On a fault condition by not limiting the current to a certain amperage there is the chance that more damage to that circuit's components will occur and irreparable damage to the TV could make it useless.
I know what would happen. The three amp fuse would blow. Any device that is plugged into a receptacle with out having sufficient resistance to limit the current flow will dead short the circuit and cause the breaker that feeds the circuit to trip. In this case the fuse being of a lower rating that the feed breaker the fuse will blow without tripping the receptacle's feed breaker.