You can use an [execute process task] to call a compression program.
here is a walk-through using 7-zip: https://www.sqlservercentral.com/articles/using-ssis-to-zip-files-and-email-the-zipped-files-1
A couple of possibilities using MS tools instead of 3rd party:
- Script Task using .NET [system.io.compression] - Powershell script ([here] is an example) called from the execute process task
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