I've just replaced the batter in my iPhone 6s, but the new one won't c

Run the new battery until it is completely drained. Then, try charging it up. If this doesn’t resolve the issue, then the replacement battery is probably faulty.

Before your phone charges the battery, it needs to communicate with it in order to know its condition (how much charge it has/needs, for example). But in order to do this, the battery has to have enough power. If the battery is completely drained for whatever reason, stayed on shelf for too long, for example, then this process can’t start. This doesn’t mean the battery is faulty, only it needs a jump start.

The way to do it is pretty simple: take it out of the phone and use a separate DC power supply to charge it. Check and adjust the voltage, monitor the current to make sure you don’t over charge or cause explosion. I usually don’t want the current go beyond 500mA.