What's the problem?
It is impossible in JIRA to restrict issue access to the employees of a particular company. It is because JIRA doesn't know what is a "company". There is no such entity.
Existing solutions
As a workaround you can try to use the Zones plugin. However, it implements a "company" entity as the JIRA group. But it complicates managing companies and doesn't give you a full-value entity of a "company".
Solution using CRM for JIRA
If using CRM for JIRA you can configure a company dictionary in JIRA. That will allow you to define a Company in the issue custom field manually, or auto-completing it by issue reporter.
To resolve the access problem you need to add unique security level principle Company People to your Security Level Scheme:
After that all people from the same company will be granted to access issues.