Travelling with car seat?? Help!

Hey mums. I have a very weird confusing question.

So I wanna take my son on holiday next summer, if everything eases down by then. But I am abit confused. So he will be turning 1 this month, which means he’s has already pretty much overgrown his car seat, which came with the 3 in 1 pram. So he will obviously need a new one.

However when we travel on holiday, we would ideally like to take cabs rather than public transport. So if I put him in a car seat in the cabs, what am I meant to do with it on the other side? When I want to push the pram for some shopping.. etc? I’m really confused. How do people take cabs with a toddler?