setTimeout($A.getCallback()) can be used to setTimeout before calling subTab() in Salesforce workspaceAPI. Check the following sample Lightning Aura Component code for reference.

Sample Code:

Aura Component:

<aura:component implements="flexipage:availableForAllPageTypes" access="global" >
   
    <lightning:workspaceAPI aura:id="workspace" />
    <lightning:utilityBarAPI aura:id="utilitybar"/>
    <lightning:button label="Open Tab with Subtab" onclick="{! c.openTabWithSubtab }" />
   
</aura:component>

JavaScript Controller:

({
   
    openTabWithSubtab : function(component, event, helper) {
       
        var workspaceAPI = component.find("workspace");
        workspaceAPI.openTab({
            recordId: '0015w0000298JM7AAM',
            focus: true
        }).then(function(response) {
            console.log( ' Parent Response is ' + response );
            setTimeout($A.getCallback(function() {
                workspaceAPI.openSubtab({
                    parentTabId: response,
                    recordId: '0035w000034EYn1AAG',
                    focus: true
                }).then(function(response) {
                    console.log( 'Child Response is ' + response );
                });
            }), 1000);
        })
        .catch(function(error) {
            console.log( 'Error is ' + error );
        });
       
    }
   
})