Utilizza font-awesome con una classe css.

codice HTML:
<!DOCTYPE html>
<html lang="it">

<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.13.0/css/all.min.css">
    <title>Document</title>
    <style>
        .search-icon {
            position: relative;
            left: -24px;
            padding: 3px;
            background: white;
            border: 0;
            color: gray;
            cursor: pointer;
        }
    </style>
</head>

<body>
    <form action="https://hard-questions.com/ricerca" method="POST">
        <input type="text" id="s" name="search" placeholder="Cerca nel sito...">
        <button type="submit" class="fas fa-search search-icon"></button>
    </form>
</body>

</html>