Since it is already given that grammar is regular grammar and $LG) \not = \phi$. So this means that for a grammar to be regular it can be either left linear or right linear. So in any of the case for left or right linear it must have a production which must terminate and give a valid string. So the grammar can be for example
$S \rightarrow aS\\S \rightarrow a \\ or \\ S \rightarrow aS\\S \rightarrow \epsilon $