Will a second hand petrol car have a lower carbon footprint than a new electric vehicle?

Yes, but only for a while.

It seems as if buying an existing, second-hand vehicle would incur a much lower carbon footprint than a brand new electric vehicle. But, the key difference between an EV and a petrol vehicle is that an EV incurs the majority of its carbon footprint during manufacture. An existing petrol vehicle will be still be pumping out emissions from its engine for years to come, so it won't actually be the more environmentally friendly option for that long. Plus, of course, an EV won't be distributing other harmful tailpipe emissions wherever it goes (which, incidentally, happens to be where people are).

Example: New 2019 Nissan Leaf

Carbon Brief have published some excellent research on this. In their example, a new 2019 Nissan Leaf is compared to an average existing conventional car. They very generously use the average CO₂ output from a conventional new vehicle (extremely likely to be higher than that, as most metrics for mpg efficiency and emissions are, optimistic to say the least. Not mentioning the $30 billion event known as Diesel Gate). Their chart shows that after 4 years, the EV has caught up with the conventional vehicle and starts cutting emissions from that point on.

There is more on this topic covered on our question Do electric vehicles produce more CO₂ than petrol or diesel vehicles?