Author comment count in author page

all you have to do is to add an param:

/* user commnet count */
function get_comment_count( $user_ID ) {
    global $wpdb;

    $count = $wpdb->get_var(
        $wpdb->prepare( "SELECT COUNT(comment_ID) FROM {$wpdb->comments} WHERE user_id = %d ", $user_ID )
    );
    return $count;
}
<?php echo get_comment_count( <USER_ID> ); ?>

PS. I’ve added some proper escaping in your query also, so this code is not vulnerable any more…

But you can also use…

WordPress already has its own way of doing it, so you don’t have to reinvent the wheel… You can use:

$count = get_comments( array(
    'user_id' => <USER_ID>, // include only comments by this user
    'count' => true // it will return only count of comments and not the comments
) );
echo $count;