Replayed your issue following the steps below:
docker run --rm -it centos:7 /bin/bash
echo "nameserver 8.8.8.8" >> /etc/resolv.conf
yum install -y epel-release
yum install -y http://rpms.remirepo.net/enterprise/remi-release-7.rpm
yum install -y php7.3-mysql
And for the last operation I got:
Loaded plugins: fastestmirror, ovl
Loading mirror speeds from cached hostfile
epel/x86_64/metalink
| 27 kB 00:00:00
* base: distrib-coffee.ipsl.jussieu.fr
* epel: mirror.infonline.de
* extras: mirror.plusserver.com
* remi-safe: remi.mirrors.cu.be
* updates: distrib-coffee.ipsl.jussieu.fr
epel
| 5.4 kB 00:00:00
remi-safe
| 3.0 kB 00:00:00
(1/4): epel/x86_64/group_gz
| 90 kB 00:00:00
(2/4): epel/x86_64/updateinfo
| 1.0 MB 00:00:00
(3/4): epel/x86_64/primary_db
| 6.9 MB 00:00:06
(4/4): remi-safe/primary_db
| 1.6 MB 00:00:06
No package php7.3-mysql available.
Error: Nothing to do
The package name you have specified does not exist, however it exists php73-php-mysqlnd, that looks pretty close to what you are trying to get.
yum search php73-php-mysqlnd
php73-php-mysqlnd.x86_64 : A module for PHP applications that use MySQL
Try with this:
yum install -y php73-php-mysqlnd