I have just brought my dad's 1996 P reg mk1 Fiat Punto 1.2 75 sx and need to replace the ignition barrel on it as there is a problem with the current one. My question though is if I buy a new barrel and key will I need to do anything with the ECU? I will still have the current Blue key (the only key for the car) as I won't be changing the door locks but i want to know can I just remove the old barrel and fit a new one?

Any advice would be much appreciated.

I did this recently cos I lost my keys and had to replace the ECU, code box and ignition barrel and locks. I take it your planning getting the barrel and key of another car in a scrappy's? if so you will need the ECU and code box aswell as the key has a code chip in it that sends to the ECU and if they don't match the immobilizer will kick in. A followed this guide and managed to pick up all the stuff at the scrappy's for £40 .
https://www.fiatforum.com/punto-guides/219588-mk1-punto-replace-ecu-code-box.html