Prior admission records, earlier visas and stamps in the old passport, any previous approval notices, and earlier employer letters describing past roles. Together these show a history of status that a newly issued passport, on its own, cannot evidence at all. Add the employer letters that describe what was actually done during each of those periods. A record proving presence without describing the work leaves the more useful half of the history undocumented.
Build the history before it is asked for
Retrieve the official admission history online and print it, then match it against the stamps in the old book so gaps and inconsistencies surface now. Check that the name spelling and date of birth agree across every record, since a transposed character discovered at inspection costs far more time than the same correction made in advance. The failure worth anticipating is a history that contradicts itself in small ways: a letter dating a role from January, an admission record showing arrival in March, a transcript issued under a former surname.
Each is explainable; together and unexplained, they read as carelessness about facts. Hypothetical example: a Medical Laboratory Technologist renews her passport, and the new book carries none of the earlier admissions recorded while she supported a clinical-trial site laboratory. She prints the official admission history, attaches scans of the cancelled book's stamp pages, and adds a note reconciling those dates with her employer letter, closing the discrepancy on paper instead of at the counter.