It depends on the size of the tablespoon. If we use a regular-sized table spoon, there are 3 tsp in a 1/3 cup, but if we use an 8 to 12-inch long cooking spoon, you would need to know how many teaspoons that equates too. Beware though – traditional tablespoons have not been standardized to 3 teaspoons and differ based on country like the UK’s tablespoon being 20 ml while our tablespoon is 25ml so both is going to be different ratios.
So if someone asked me for a third of a teaspoon I would give them one fifth or one sixth depending on where I am from as well as whether we’re talking about this type of measuring spoon or some other type of metric scale.