What are some DIY tips for fixing a leaky faucet?
Putting in a new cartridge will help, but you have to have the right tool and be strong enough to remove the old one. Unfortunately, I was not that person and a plumber had to do it for me.
Depending on exactly what's being replaced, if the shutoff valve is close to the tap (and ideally it would be) you may be able to very gently turn the water pressure up and let it push something out. I did that when I couldn't get a good grip on the piece I needed to remove and didn't want to risk damaging it by gripping and pulling with a big wrench. It didn't take a lot of water behind it to push it out, and as soon as it moved I turned the water off again.