The DataTables JavaScript library has a Column Filter plugin that allows to add filtering boxes to the table foot row.

To use this in your tables, download, install, and activate this Extension like a regular WordPress plugin. Then change your table’s Shortcode from something like

[table id=123 /]

to

[table id=123 datatables_columnfilter="true" /]

If this Extension is helpful for you, please consider supporting further TablePress development with a donation. Thank you!