Currently, when Exporting Search Results to Excel, the user interface by default only allows a user to export a maximum of 1000 issues to an excel spreadsheet.
For JIRA Server - allow admins to increase the limit
For JIRA Cloud - Consider slightly increasing the limit, provided the Cloud Server can handle the increase
For Behind the Firewall Customers
Please consult the KB article at Export More than 1000 Results to Excel
For Cloud Customers
Please consult the KB article at Cloud - Export More than 1000 issues to Excel from Issue Navigator