Chargent will only be able to sync transactions that are already created in Salesforce. For past transactions that were initiated via your Payment Gateway, you would need to migrate those transactions over to Salesforce. Once the transactions are migrated into Salesforce future transactions will be able to be sync'd as expected.
If you are using Recurring Billing you also want to make sure the Recurring Billing fields are populated correctly, an Apex batch is scheduled in Salesforce, and tokens are present to process the charges. This will allow future payments to continue as expected and update.
Not all Gateways allow for Transaction Sync. For more information on what is needed to sync transactions including what gateways allow the sync, please check out our article