Posting on behalf of customer:
It would be great to restrict the ability for users to update associations - so for example, restrict the ability to remove an association from a record - whether it is custom objects or standard objects.
The customer would like to Add Permissions to the feature to Add new associations or existing ones on a Record to Owner Only/Super Admin/Team Only. This is to prevent multiple false creations of associations.
Yes, this decreases issues, especially on the ownership of the contacts, deal creation, and sales.
this is 100% necessary particularly as a company grows they will need the added functionality 
Not trying to hijack this thread, but I think, in general, more granularity in permissions is necessary, including better control over viewing association cards…not just adding/removing associations. Currently if a user doesn’t have visibility of the entire target record (e.g., a Deal), they can’t even see that record’s association card on a related record (e.g., they can’t see the Deal card on an associated Company record.)
See this post for my real-life example of how this is creating major headaches!
Hello! My name is Hallie, and I’m an Associate Program Manager on our CXM team here at HubSpot. I’m happy to share that there is now a beta feature for association permissions! You can read more about this feature here. Please continue to leave feedback as you use the beta for our product teams! 
Thank you for the update
Thank you very much @hhiggins!
I find the feature a great addition to the HubSpot ecosystem. However, some of my customers require more granular control. For example:
- One customer needs to prevent the removal of associations, but only for a specific custom object.
- Another needs certain users to be able to edit associations, while restricting this for others.
- And 4 customers require users to be able to add new custom object records only, without permissions to edit or remove them.
In my opinion, the feature would be even more valuable if permissions could be customized per action and object type.
Empty
Agreed with the above - more granular control would be fantastic. I want to provide clients the option to create associations of a particular type, only for Contacts to Companies, but don’t want them to mess with Company-to-Company associations unless through a specifically designed UI Extension.