According to your description, my understanding is that you want to know how to start a 2010 workflow in SharePoint 2013 workflow.
To start a 2010 workflow in SharePoint 2013 workflow, SharePoint 2010 workflow should be ready for run at the moment it is called, which means that it needs to be already associated if it is a Reusable workflow. Hence, these are supported
by a single action “Start a List Workflow” which receives 3 parameters: the SharePoint 2010 associated workflow to be triggered, initiation form parameters, and target item the associated workflow will run on. On the contrary, Site workflow does not need an
item to run on so rely on another action “Start a Site Workflow” which receives 2 parameters: the SharePoint 2010 site workflow to be triggered, and initiation form parameters.
Here are some links about how to implement this in SharePoint Designer for you to refer: