First of all, don't do this. It's frown upon and in a way, it makes sense since it kinda defeats the purpose of docker to begin with.

However, there might be situations in which is justified and then this will come handy.

cat .tmp/default.db | docker exec -it postman_postman_1 bash -c 'cat > /opt/postman/.tmp/default.db

If you happen to get the following error:

cannot enable tty mode on non tty input

Just remove the t flag from docker exec -it:

cat .tmp/default.db | docker exec -i postman_postman_1 bash -c 'cat > /opt/postman/.tmp/default.db