Need additional travel insurance if Miles credit card cover complimentary insurance?

Hi, you I think you could first try to understand what your credit card's travel insurance covers. I think this article might be helpful to you in identifying what other factors are important to you that may / may not be covered by your card's travel insurance.

Suggest you read the terms of the complimentary insurance and the ease of claims to see if this is something you are comfortable with. If that answer is no, then apply for additional travel insurance.