How does travel insurance claims for travel cancellation works? My partner have an important meeting and could not make it for our trip during September later this year. Only flights have been booked.?

You need to take a clear look at the travel insurance product factsheet. Most of the cancellation clause only covers hospitalisation or extraordinary events such as natural disasters or terrorist attacks and exclude perisonal reasons. I highly doubt that a doctor memo would suffice. What you can do is to try to sell your air tickets away on Carousell.