One way of doing this is with the use of https://www.drupal.org/project/eva which lets you attach any entity to any other entity
Just for demonstration I have setup
parent 1 child 1.1 child 1.2 parent 2 child 2.1 child 2.2
install and enable eva create a taxonomy terms view called children with no block or page display

Then add an EVA views display from the dropdown You will need to set a contextual filter parent term with following settings
Hide when value not available specify validation criteria taxonomy term id: [NAME-OF-VOCABULARY] hide view

and on entity content settings set entity type: taxonomy term and bundle: [vocabulary name]
I had to clear cache so it does not hurt to do it and visit any of the taxonomy parent pages you should see the children terms

you can change where the children are displayed at your taxonomy term display settings page
