taxonomy_set_lineage

This module will automatically add all parent terms to the field values for each term in an entity's taxonomy reference fields.

An example use case would be a Geography taxonomy containing all continents, countries and cities in a tree structure. Without this module, when a user tags content with Berlin, the content would not be able to be found under Germany or Europe and those parent tags would not appear on the content page.

This module will make sure that these parent terms are also selected when the content is saved.

How it works
If any vocabularies have lineage set, we check entities when they are saved to see if they have fields referring to these vocabularies. If so, we automatically select all parent terms of manually selected terms.

Note that this does not override the maximum number of terms selectable in a field. If a field restricted to only one term this module will not be able to set any parent terms in that field.

This module should work with any drupal language / i18n / localization strategy.

Bulk operations/actions
The module provides an Update Taxonomy Term Parents action that can be applied to selected entities on the content administration page.

This will add any missing parents to the selected entity's taxonomy reference fields. This will not remove any of the existing values. This means if you edit your taxonomy and move a term to a different parent, the new parent will be added but the previous parent will still remain in the list of values.

Other taxonomy modules:
Hierarchical Select - provides a hierarchical selection widget for Drupal 7 which includes saving of lineage.
Taxonomy Term Reference Tree Widget - provides a tree widget for Drupal 7, 8 and 9.
Simple hierarchical select - provides a hierarchical selection widget for Drupal 9 - does not save lineage.
Client-side hierarchical select - provides a hierarchical selection widget for Drupal 9 and includes the option to save lineage.