pancham kumaris right, digital print needs a different ICC profile to offset print.
However I still believe that display screen calibration comes first.
Also you mentioned "printing on A4 paper" does that mean you are printing "in house", maybe on your own inkjet printer?
Even if that’s the case, you need to first pay attention to your display setup (calibration and profiling) . The screen appearance sets your expectations for the work you produce.
Next, for an inkjet printer you need a profile for that printer and the paper (and inkset) you're using.
If you are using the printer manufacturers original ink - I suggest you start by making an easy test using a printer manufacturer's own paper - why? - because this allows you to set the Adobe application to "printer manages color" - now when you select the paper (media) type in the printer driver dialog boxes that setting will tell the system to use an ICC profile for that paper.
To do this test properly you need a testimage that’s not been adjusted on your screen (which may be misleading you, as I explained earlier). I suggest you download this one: http://www.colourmanagement.net/downloads/CMnet_Pixl_AdobeRGB_testimage05.zip which is an RGB image. The system will read the embedded ICC profile and make a conversion for you to the printer ICC profile during printing.
using the process I described above, you should get a decent print. As that testimage has skintones and other ?memory colours" its pretty easy to see if it's looking OK.
So that’s a step in the right direction.
Now compare that print to your screen, does your screen look way different? If so its very likely it needs calibration.
I hope this helps
if so, please do mark my reply as "helpful" and if you're OK now, please mark it as "correct" below, so others who have similar issues can see the solution
thanks
neil barstow, colourmanagement