See https://wordpress.stackexchange.com/q/360588 for details.

functions.php

<?php
function updated_tos_agree_submit() {
	$errors = array();

	// Validate the submitted form data.
	if ( empty( $_POST['tos_agree'] ) ) {
		$errors['tos_agree'] = 'You must agree to the Terms.';
	}

	if ( ! empty( $errors ) ) {
		// Store the errors in a transient - a temporary option in the database.
		set_transient( 'my_form_errors', $errors, 30 );

		set_transient( 'my_form_data', array(
			// Put relevant submitted form data here.
		), 30 );
	} else {
		// Update User Meta here.

		// Delete the errors transient and add a success one.
		delete_transient( 'my_form_data' );
		delete_transient( 'my_form_errors' );
		set_transient( 'my_form_success', 'true', 30 );
	}

	// Redirect back to the form page.
	wp_redirect( wp_get_referer() );
	exit;
}
add_action( 'admin_post_nopriv_updated_tos_agree', 'updated_tos_agree_submit' );
add_action( 'admin_post_updated_tos_agree',        'updated_tos_agree_submit' );

template.php

<?php
// This is false if there has been no submission (i.e. the request method
// is GET) or that there are form validation errors (from admin-post.php).
$settings_updated = false;

// Get the form errors, if any.
$errors = get_transient( 'my_form_errors' );

// Then display the errors above the form or wherever else that you prefer.
if ( is_array( $errors ) && ! empty( $errors ) ) {
	echo '<ul class="form-errors">';
		echo '<li>' . implode( '</li><li>', $errors ) . '</li>';
	echo '</ul>';
} elseif ( ! empty( get_transient( 'my_form_success' ) ) ) {
	$settings_updated = true;
	delete_transient( 'my_form_success' );
}

if ( ! $settings_updated ) :
	$data = get_transient( 'my_form_data' );
	// So you'd use $data['<name>'] instead of $_POST['<name>'] to get the submitted data.
?>
	<form action="<?php echo esc_url( admin_url( 'admin-post.php' ) ); ?>" method="post">
		<label for="tos_agree">
			<input type="checkbox" name="tos_agree" id="tos_agree"
				<?php checked( true, ! empty( $data['tos_agree'] ) ); ?> />
			Some text for the checkbox
		</label>

		<button type="submit" name="agree" value="I Agree">I Agree</button>

		<input name="action" type="hidden" value="updated_tos_agree" />
	</form>
<?php else : ?>
	<p>Settings updated.</p>
<?php endif; // end $settings_updated ?>