What's the problem?

It is impossible in JIRA to restrict issue access to the employees of 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 Zones plugin. However, it implements "company" entity as 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 mannually, or auto completing it by issue reporter.

To resolve the access problem you need to create custom field with Multiuser-picker type and add it to the Issue Security Scheme of your project.

Then you need to select this field in the Company configuration of CRM Plugin.

After that the field will be automatically filled in with the company's contacts in JIRA issue and will give private issue access to this contacts.

 When adding/removing a contact to/from the Company all the changes will be applied to already created issues.