As a contract QP you are a “normal” contracting party (i.e. just like any other service provider for the company but with the specific legal responsibilities and risks of a QP) and therefore no employee of the company. That means that you are not covered by any of the insurance programmes which companies usually provide for their employees (e.g. D&O insurance). As a result, you should mention that fact – and the related legal risks – during your contract negotiations with the company.
Ideally, there should be an indemnification clause in the service contract providing for that ‘the company indemnifies the contract QP any and all third party claims related to the services which the contract QP may perform under the service contract’. If your current contract does not contain such provision, you should ask the company to sign an amendment with aforesaid clause.
You can also ask the company to get yourself explicitly included in its D&O insurance contract (some insurers may actually be ready to do so because of the specific situation of the contract QP).This inclusion could be the first part of the contractual provision, followed by the indemnification clause mentioned above.