Update existing containers

Hi
I am looking at rebuilding some of my existing apps to run as microservices using docker.
Most of these do run on PHP and therefore I am using the official PHP images.
There is however one slight problem and that is the PHP images compile a specific version of fx. PHP 7.3 and then I have to manually update it when a new 7.3.x release comes out.

Is there an easy way to rebuild my custom docker image, when a new PHP-version comes out, and deploy that to all running containers or would I need to destroy the containers and then recreate them using the newly built image to get updated versions?