To synchronize time tracking fields such as Original estimate, Remaining estimate or Time spent you need to add following scripts into the corresponding synchronization processors. Setting the time spent in Jira Cloud directly is not supported, it needs to be set through worklogs.
Source Instance
Outgoing sync
Send Time tracking information to the Destination Instance.
// Add the time tracking information to the datafilter replica.timeSpent = issue.timeSpent replica.originalEstimate = issue.originalEstimate replica.remainingEstimate = issue.remainingEstimate
Destination Instance
Incoming sync
Apply received Time tracking information from the Source Instance.
// this will overwrite the current time tracking information issue.timeSpent = replica.timeSpent issue.originalEstimate = replica.originalEstimate issue.remainingEstimate = replica.remainingEstimate