If your home page represents a local business or one of the following types and has the appropriate structured data, then user reviews about your business can be presented by Google in rich results with stars. Check the following google recommendations for type Review:
You can supply ratings for the following content types:
Refer clearly to a specific product or service by nesting the review
within the markup of another schema.org type, such as schema.org/Book
or schema.org/LocalBusiness, or by using a schema.org type as a value
for the itemReviewed property. Make sure the reviews and ratings you
mark up are readily available to users from the marked-up page. It
should be immediately obvious to users that the page has review
If the review snippet is for a local business, you must follow these
Ratings must be sourced directly from users.
Don't rely on human editors to create, curate, or compile ratings
information for local businesses; instead, use critic review
structured data. Sites must collect ratings information directly from
users and not from other sites.
It may also be useful for you to check the following Google recommendations from the guide Follow the structured data guidelines:
Don't mark up irrelevant or misleading content, such as fake
Google’s guide on spam in structured data also has interesting information:
Review written by the site or person providing the service Reviews
must not be written or provided by the business or content provider
unless they are customer, independent, and unpaid editorial reviews.
Thus, your structured data from the third-party TrustPilot website may be deemed irrelevant.