Using a trigger code in the calendar event for a specific project task within Harvest will create log that task in time sheet.
If
Event from search starts
This Trigger fires a set number of minutes before the starting time of an event on your Calendar that contains a specific keyword or phrase in the event’s Title, Description, or Location. Ingredient will be based on the zone set in Google.
Then
Create task in project
This Action will create a new task in the project you choose. NOTE: You must be an Admin in Harvest to do so.
Explore more great ways to automate Google Calendar and Harvest