So, most of my docker compose scripts are fairly specific, Most are using the :latest tags unless there is a specific reason for not doing so. Updating them can be carried out periodically by running the following

#Once SSH'ed into the hosting server

docker compose pull 

#Alternatively, if using profiles

docker compose --profile chosen-profile pull

#If it does pull down any new versions, then stop the
#current containers, build, then restart

docker compose --profile chosen-profile down
docker compose --profile chosen-profile build
docker compose --profile chosen-profile up -d

#For issues, leave off the -d switch to see startup messages. Failing that 
#investigate the logs of the containers

docker logs name-container