The php-mbstring is part of Redhat's server optional packages. If you have a current subscirption all you need to do is to enable this repository using:
[root@rhel7 ~]# subscription-manager repos --enable=rhel-7-server-optional-rpms
and use yum to install php-mbstring. In case that you do not have a current Redhat subscription you can install php-mbstring directly from IUS project repository:
This is a companion discussion topic for the original entry at https://linuxconfig.org/installation-of-missing-php-mbstring-on-rhel-7-linux