One of the largest barriers to people leaving reviews is that they aren't a 'member' of the channel you want them to leave a review on. If you can get them to follow you on that channel, you have a greater chance of getting them to take action.
For instance, if they requested service with a Gmail address on your contact form, you know that they can easily leave a Google review. You might leave in your email signature a quick link for them to "leave a Google review".
Pro-tip: Did you know Google finally fixed that annoying “no direct url to leave a review” thing? Now, if you manage your “Google my Business profile” you can customize it. See? https://g.page/StraTacMarketing/review
If in your customer service interactions you ask customers follow you on Facebook, you can make a blanket request to your audience to 'share your experience with ______, we value your feedback!"
When you phrase it as “feedback”, rather than 'review' you open yourself up to being able to take intel from the information those people share. Also, it keeps you from violating the rules against “requesting reviews”.
Remember, this is a great way for you to capture the voice of the customer so you can make business decisions based on true customer feedback.