Do I have to charge HST to a client who lives outside Canada for services I provide from Ontario?

Generally, no, many services supplied to a client who is a non-resident of Canada are zero-rated under the Excise Tax Act, meaning GST/HST applies at a rate of zero rather than at Ontario's 13%, provided the specific conditions for that zero-rating are met. Being physically based in Ontario as the supplier doesn't change this outcome; what matters is the client's non-resident status and the nature of the service, not where you personally perform the work.

The conditions for zero-rating aren't automatic just because the client happens to live abroad, though, there are specific exceptions and requirements depending on the type of service and how directly it relates to Canada. A service connected to real property located in Canada, or one delivered to the non-resident client while they happen to be physically present in Canada at the time, are examples of situations where the general non-resident zero-rating may not apply the way it would for a straightforward service delivered entirely to someone outside the country.

Because the specific type of service you provide, and the client's exact circumstances, determine whether zero-rating actually applies, confirm the correct HST treatment with a tax advisor for your specific service rather than assuming every non-resident client automatically means no HST.