Since a teaspoon is a measurement of volume and a gram is a measurement of mass, it's not possible to convert from one unit to the other without knowing what substance is being used. When comparing teaspoons of different substances, the one that is denser will weigh more.
For example, 1 teaspoon of granulated sugar weighs about 4.67 grams, but 1 teaspoon of confectioner's sugar, which is used to make icing, weighs around 3.67 grams. This is because granulated sugar is denser, meaning it weighs more despite being in the same-sized container. Even then, the number is approximate, because the precise density is still unknown.