I would like to know what is this instrument that is above the EGT of the Boeing 737. What does it indicate?
This is a differential pressure and cabin altitude indicator.
The outer dial indicates the difference in pressure between the inside of the cabin and the outside in psi. During takeoff and landing, it must not be larger than 0.125 psi, as the note below the instrument says. If it exceeds 9.1 psi, the pressure relief valve will release the pressure to prevent damage to the airframe:
Two pressure relief valves provide safety pressure relief by limiting the differential pressure to a maximum of 9.1 psi. A negative relief valve prevents external atmospheric pressure from exceeding internal cabin pressure.
(Boeing 737 NG FCOMv2 2 - Air Systems - Pressure Relief Valves)
The inner dial shows the cabin altitude in thousands of feet. During normal operations, it should not exceed 8,000 ft. This is a measure of the absolute pressure inside the cabin, converted to an altitude using the standard atmosphere (ISA) pressure profile.
Note: The instrument below is typically a cabin climb indicator showing the rate of change of cabin altitude in thousands of feet per minute:
(image cropped from here)
The EGT instrument in your image shows the Exhaust Gas Temperature of the APU and is typically installed further to the left on the overhead panel.
As per this article, it's a Cabin & Differential pressure gauge (Boeing).
Here's an explanation:
The differential pressure gauge shows the difference between the pressure inside the aircraft and the pressure outside. So you would expect that diff pressure would be zero when you are on the ground and the passengers are boarding. When you are climbing, in cruise and arriving, the diff pressure shuold be positive; basically it should increase as you climb since the pressure outside decreases but the pressure inside remains the same (it decreases as well but not as much as the outside). On final you should again have the zero diff pressure.