Hi there,
I believe that the association you are referring to is already available, you would just need to modify the schema for your Custom Object.
To add other associations to your custom object, use: POST https://api.hubapi.com/crm/v3/schemas/{objectType}/associations. You can only associate your custom object with standard HubSpot objects (e.g. contact, company, deal, or ticket) or other custom objects.
The kb article below shows that the Custom Object(Contractors in the example) can appear in the right hand side bar in exactly the same way as Deals & Tickets.
This is found in the developer docs here;
And in the below kb article you can see that Custom Objects can sit in the right hand side bar in the same way as Deals & Tickets and you can define what data is previewed here.
I hope this helps