Magento1: How to set a dependency in a system XML of new extension

As far as I understand what you need, you should use <depends tag, example from app/code/core/Mage/Paypal/etc/system.xml:

<payment_action translate="label">
    <label>Payment Action</label>
    <config_path>payment/paypal_express/payment_action</config_path>
    <frontend_type>select</frontend_type>
    <source_model>paypal/system_config_source_paymentActions_express</source_model>
    <sort_order>30</sort_order>
    <show_in_default>1</show_in_default>
    <show_in_website>1</show_in_website>
    <shared>1</shared>
</payment_action>

<authorization_honor_period translate="label comment">
    <label>Authorization Honor Period (days)</label>
    <comment>Specifies what the Authorization Honor Period is on the merchant’s PayPal account. It must mirror the setting in PayPal.</comment>
    <config_path>payment/paypal_express/authorization_honor_period</config_path>
    <frontend_type>text</frontend_type>
    <sort_order>50</sort_order>
    <show_in_default>1</show_in_default>
    <show_in_website>1</show_in_website>
    <shared>1</shared>
    <depends><payment_action>Order</payment_action></depends> <!-- see this line -->
</authorization_honor_period>

Dependencies can be set in your app/etc/modules XML. Magento will check if the extension is available.

<?xml version="1.0"?>
<config>
    <modules>
        <Your_Extension>
            <active>true</active>
            <codePool>community</codePool>
            <depends>
                <3thparty_Extension/>
            </depends>
        </Your_Extension>
    </modules>
</config>

Or use the following code to check if an extension is enabled. This can be done by creating a helper method in Namespace/Module/Helper/Data.php

class Namespace_Module_Helper_Data extends Mage_Core_Helper_Abstract 
{

   public function extensionEnabled()
   {
      return Mage::getStoreConfig('advanced/modules_disable_output/Namespace_Module');
   }
}