Grodd is to Lex Luthor as the Wingless Wizard is to Doctor Doom. He's different enough to be recognizable, but too similar to be anything other than second-rate. And a megalomaniac ape with telepathy and genius-level intelligence shouldn't be second rate.
The thing writers often forget about Grodd is that he's not just smart-he's smart. He works through catspaws and hired guns to accomplish his goals, which are, for the most part, opaque to his enemies and allies alike. No one knows what Grodd wants, except Grodd.
That's where writers stumble, unfortunately. Grodd's driving ambition is domination...but of what? The world? Gorilla City? It tends to change depending on the creative team. Sometimes he wants to turn everyone into gorillas, other times he wants political power. Thing is, none of these are short-term goals...they're all master plans. And they're all just generally sort of megalomaniacal. Luthor, Doom, Darkseid, Thanos...all the great plotters have a set end game. The reason they resonate so strongly is because we know what they want and we know that everything they're doing is directed at accomplishing that one goal. So why not Grodd?
Of course, that means you have to come up with said goal-for Grodd, I'd say stick with Gorilla City. Grodd wants nothing more (or less) than to assure the safety and supremacy of his people. He's a patriot (or terrorist), and he's at war with everyone who isn't a citizen of Gorilla City. Grodd should be the Magneto of the DC Universe, defending a small minority against a hostile (to his eyes anyway) majority.
Grodd should be using his telepathy to hide his involvement in his schemes and meeting with the UN as Gorilla City's official representative, where he'll sow discord and reap the benefits. He'll hire super-villains to attack him, in order to appear the victim of anti-gorilla discrimination. He'll assassinate his own people if they stand in his way, and kill humans without a thought. He'll fund terrorist groups and rebel organizations in the Congo, Nigeria, etc. in order to strengthen Gorilla City's position on the African continent. He'll work with the Cheetah to retrieve ancient Gorilla artifacts from private collectors and unleash the Giggling Plague on Lagos. He'll hire an assassin to strike out at King Arthur of Atlantis and then foil the attempt in order to further the possibility of an alliance.
And he'll do it all for the good of his people. Whether they appreciate it or not.