Linked record fields have multiple permission levels. For example, the parent field (on the form) can be read-only (i.e. not allowing users to create, link or unlink records) but the child form is editable (or vice versa). There are different methods for setting this up for different use cases:
Allow users to view/edit linked records, while not letting them change which records are linked
Open the linked record field's settings
Go to the Record Finder Options
Under Record Finder Mode, select Hide record finder button
Make sure that Allow users to unlink existing records is turned off
Go to the Create & Expand Records section
Turn off Allow users to create new records (if desired)
Turn on Allow users to expand (or edit) linked records
Click on Edit Form to open the child form for expanding linked records.
Click on Bulk Actions and make all read-only to prevent edits to fields within linked records (if desired).
Do not allow users to open linked records, or changing which records are linked
Open the linked record field's settings
Turn on read only.