Wordpress - Hide the term description on the term edit page, for a given taxonomy

You could target the edit form for the post_tag taxonomy, through the post_tag_edit_form hook:

/**
 * Hide the term description in the post_tag edit form
 */
add_action( "post_tag_edit_form", function( $tag, $taxonomy )
{ 
    ?><style>.term-description-wrap{display:none;}</style><?php
}, 10, 2 );

Here you can also target an individual tag.

If you need something similar for other taxonomies, you can use the {taxonomy_slug}_edit_form hook.

Update

It looks like the question was about the list tables, not the edit form.

I dug into the list tables in WorPress and found a way to remove the description column from the term table in edit-tags.php

/**
 * Remove the 'description' column from the table in 'edit-tags.php'
 * but only for the 'post_tag' taxonomy
 */
add_filter('manage_edit-post_tag_columns', function ( $columns ) 
{
    if( isset( $columns['description'] ) )
        unset( $columns['description'] );   

    return $columns;
} );

If you want to do the same for other taxonomies, use the manage_edit-{taxonomy_slug}_columns filter.

The cleanest way to do that, removing the description field from the edit screen also in the add screen:

function hide_description_row() {
    echo "<style> .term-description-wrap { display:none; } </style>";
}

add_action( "{taxonomy_slug}_edit_form", 'hide_description_row');
add_action( "{taxonomy_slug}_add_form", 'hide_description_row');

Of course you need to replace {taxonomy_slug} with your taxonomy slug.

If you also need to hide the description field in the add form use this code

/**
 * Hide the term description in the edit form
 */
add_action( '{taxonomy_slug}_add_form', function( $taxonomy )
{
    ?><style>.term-description-wrap{display:none;}</style><?php
}, 10, 2 );