Hi @Repowering
If the custom property is a Text String or a Dropdown, HubSpot will update the contents of the property if a value is present in it in the import file. If there is no value against a contact, the current value will remain.
Is is possible to append the values in a multi-checkbox property however: Import data to checkbox properties
If this is not suitable, thrid party services or intergrations might offer a solution. There is an idea thread discussing the issue and some possible solutions, I suggest you vote on it: Update/Overwrite/Append Data Options for Contact Property Fields
Hope this helps.