How to install Social Auth LinkedIn PHP Library with composer for Open Social Drupal module?
According to the composer.json of that module, you need happyr/linkedin-api-client. So to install that with Composer, from the root of your Drupal project run:

composer require happyr/linkedin-api-client:1.0.0


Since that library has dependencies too, you probably need to install them too. Basing on the documentation, you could need to execute the following too.

composer require php-http/guzzle6-adapter
composer require guzzlehttp/psr7 php-http/message