Does the brain have a clock and can it be sped up?
While the brain is often compared to a computer (sometimes even rightfully), one key aspect people often overlook is that the brain is inherently analog, whereas computers are inherently digital:  

All a computer really does in any single operation is to combine 0's and 1's really really fast - and the faster it's able to do that, the faster it will generally be. 

A brain however, fundamentally works by combining a multitude of signal inputs with varying strength's and each single operation (encoded by a single neuron) will give output depending on the weighted sum of all inputs.
Such a 'single operation' in itself is reasonably fast, whats make a brain 'slow' is the propagation of the signal to next neuron/operation: Brains are orders of magnitudes bigger than computer chips and instead of metal/wires they use concentration gradients to propagate the electrical signals. Of course it's possible to increase the speed on individual connections between neurons by insulating them, which nature already does.

However, you can't just 'overclock' the whole brain, because there's simply not enough space to add 'full insulation' to every single connection between two neurons (of which there a lot: ~100 billion neurons, with a couple thousand connections each) and because electrical signal propagation by concentration gradients will always be slower than by wires.

I guess if would replace all neuronal connections with metal wires and some concentration gradient to power/voltage/frequency converter using nanobots, you could potentially speed up the brain - or just built cyborgs instead.

Also, not really what you asked  -  but there IS a clock in the (mammalian) brain and changing it speed, will seriously mess with your day/night or sleep rhythm.