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
