I'm not sure that there is one. Researchers in every subdiscipline have their own, and plate tectonics has tied everything together enough that there aren't as many huge overarching questions that everyone is waiting for an answer to.
Some big ones:
How and why does magma travel through the crust and how does it accumulate in enormous bodies? Does it do so in small batches, displacing the rocks outside? Does it do so in huge batches, melting and incorporating the rock that it takes the place of? Why does (more dense) basalt magma rise through (less dense) continental crust?
Are tectonic plate velocities constant over 10 to 100,000 year timescales? Do the faults that are the boundaries between these moving blocks of crust slip at a constant rate (i.e. do the rocks on either side of a fault move at a constant relative velocity)? This relative movement produces earthquakes, so we also want to know if the rate of earthquake production is constant, and if big earthquakes are quasi-periodic (happening regularly spaced in time, with a similar magnitude) or if they are random (happening randomly but with a constant mean rate, like a Poisson process). Observational evidence suggests that big earthquakes on nearby faults are clustered in time, but we don't have good statistics for it because the data are sparse and a lot of data get erased by geologic processes, and we don't have good mechanical models for why this would happen in the first place.
How and why do huge plateaus such as Tibet and the Altiplano form? Do they pop up in a broad swath, or do they form like a narrow mountain range and then grow outward? What controls this?
How does the development of topography affect weather and climate, and how do weather and climate affect topography? For example at a local scale, concentrated erosion due to landsliding from topography-induced precipitation can impact where and how fast faulting and earthquakes occur by altering the force balance in the upper crust. On a more broad scale, the development of mountain ranges increases the rate of weathering and erosion of minerals which alters the CO2 budget of the atmosphere and sea, which changes climate.
How do geological events affect the ecology of an area and the world, and how do changes in ecology affect geology? Grasslands erode very differently than forests. The development of land bridges between continents causes exchanges in flora and fauna that can radically alter ecosystems.
So many of these questions aren't like we think of physics in the 20th century, where a singe discovery alters the field and everyone wants to do that thing. It's more like complex systems science where affects everything else and we want to see how.