Yes, you typically can add your employer as an additional insured on your personal auto insurance policy if you need to. This is a somewhat normal request if you use your personal vehicle during work hours.
For your knowledge, an Additional Insured is a person or an organization, other than the named insured or covered person, who is protected under the named insured's auto policy. If an auto is leased, the leasing company may want to be listed as an Additional Insured as well as a lien holder or loss payee. This protects the leasing company if it's named in a lawsuit for an accident caused by a policyholder.
So in basic terms an additional insured is any entity, not shown in the part of the declarations page showing the named insured, that is provided Liability protection on an insured's insurance policy. Speak to your insurance agent about adding your employer as an additional insured which may be done with an endorsement.