I have just replaced the fuel pump on my 2007 Nissan Tiida (Versa) and now I have P0171 error and engine light on. Could the fuel pump be causing this error or should I be looking elsewhere? The car does not always start as it should, and runs rough at times. Some days it is OK but others it has a lot of trouble with low fuel symptoms.

The P0171 is a Fuel Injection System Malfunction, look in the FSM for troubleshooting this issue.
https://www.nicoclub.com/FSM/Versa/2007/hatch/EC.pdf starting on page 276

Might be something as simple as a dirty fuel filter, has it ever been changed?

You could also try cleaning the MAFS (with MAFS cleaner)

PO171 is a system lean code. I once had that code on a Ford Escort when the 02 sensor was bad but a common cause of PO171 is a vacuum leak where un-metered air is getting into the system and causes a the ECU to throw a lean code. Has your fuel mileage been worse lately? Often when it throws that code the ECU will dump extra gas trying to overcome the lean condition. I've got the same code on one of my cars now and I'm pretty sure it's a vacuum leak because the engine will occasionally stall. When the weather clears up I've got to try to hunt down a the vacuum leak. My fuel mileage on that car is down about 2-3MPG.

A lean code typically does not show until the ECM has run out of ability to richen the motor up.

OP does not say if pump was brand new or a used one...........if used it could easily be the pump.