What happens after an electron and hole combine? OK so I understand that an LED is a pn junction where when a forward bias is placed across the junction, the electric field causes the electrons to combine with the holes and release a photon through radiative recombination.
Now after the electron has combined with the hole what process leads to their re-separation so that more photons can be generated?
 A: N type semiconductor material has mobile electrons; P type semiconductor
material has a nearly-full band of electrons, which form a kind of log-jam: the
only mobility is due to the occasional voids in the band, called 'holes'.
Movement of an electron, from conduction band in an N region to a P region, is current induced in the LED by the battery (or other power supply).
That newly arrived electron is in the unstable state of being in
a high energy band while vacancies in the lower band (holes) are
prevalent.  When it drops from the conduction band into a hole in the valence band, that's called 'recombination'.  By conservation of energy, we
can expect to see a single photon that can escape the material as light (of a hue that represents the energy difference in those bands).
As to how the electron gets uncombined, that happens at the wire connection
(the positive terminal of the LED) as a steady flow of negative charge
goes into the wire and through the generator/battery/power source, into
a second wire, which connects to the negative terminal of that LED.
The wire-to-semiconductor connections are just as eventful as the light-emitting
PN junction, in their own way, but without emitting light.  That is because the
large  number of filled states, and large number of vacant states, in the 
conduction band of a metal, allow for many thermal-energy-sized energy hops instead of one big leap across a bandgap.
A: Basically the forward bias has increased the energy of said system and the pair falls back to the lowest energy state
A: In a semiconductor when an electron leaves its position in the arrangement of atoms  and becomes a free carrier, its former position which is now a vacancy can be treated as  a +ve hole.
So in the structure two types of carriers get created  which move in opposite  direction when an external potential is applied.
In normal thermal motion these carriers  diffuse and collide with atoms and other carriers
At any temperature the number of holes and electrons are equal but due to thermal motion and diffusion  process whenever an electron falls in a hole a 'recombination' can be said to have happened .
As the energy of electron and holes are different the recombination leads to emission of light of various colors depending on the band gap of the material of the diode.
After recombination the site where the pair was created becomes neutral but fresh electron -holes pair get  created and the process  continues.
In some diodes the electrons also dissipate their thermal energy in the form of photons
For a detail discussion the references are given  below

References: http://www.allaboutcircuits.com/textbook/semiconductors/chpt-2/electrons-and-holes/:
https://en.wikipedia.org/wiki/Light-emitting_diode), section "working principle":

