In the beginning it is a chicken-egg problem, right? In order to link a comment item to a parent item you need to know the parent-items _id value. Which you only get after you created the parent-item.
And to link the parent-item to the comment-item you need to know the comment-items’ _id, again only available after the comment-items’ creation.
So the process seems to be
- POST create-parent-item without comment link
 
- now 
parent-item._id is known, e.g. 6128aa4e3630618af4000188 
- POST create-comment-item with
 
{
  "parentLink": {
      "_id": "6128aa4e3630618af4000188",
      "link": "parents",
      "display": "entry 1"
  }
  ...
}
- now 
comment-item._id is known, e.g. 6123b44c6138326b83000331 
- GET parent-item current object to have the latest version of it
 
- extract and extend 
commentsLink array by new reference to new comment-item (I assume this is a 1:n multilink relationship) 
{
  "commentsLink": [
      {
          "_id": "6123b44c6138326b83000331",
          "link": "comments",
          "display": "comment 1"
      }
  ],
  ...
}
- POST update-parent-item 
/api/collections/parents/save 
// param "data"
{
  _id: "6128aa4e3630618af4000188",
  "commentsLink": [
      {
          "_id": "6123b44c6138326b83000331",
          "link": "comments",
          "display": "comment 1"
      }
  ]
}
BUT be aware, that due to the asynchronous nature of those request this scenario bears a high risk of race conditions where 2 comments at the same time get not properly linked, because they update the same parent item at the same time.
A cleaner solution would be to only save the parents-link in the comment-item when creating the new comment-item and then have a custom script triggered on-comment-item-save to update the links in the related parent-item.
And in order to avoid repeating the race-condition-out-of-sync (only on a smaller scale) issue you might not only want to just add the current comment but “all lately (within the last seconds) created, related and not-linked-in-parent-yet” comments.
And maybe I overshot here.
But my answer to your question
You do this by having the collectionlink fields data added into your HTTP POST requests.
First into the comment-item:
- POST 
/api/collections/comments/save + data=NEW_COMMENTS_OBJECT_WITH_COLLECTION_LINK_FIELD_DATA 
And then as an additional update to the related parents object
- POST 
/api/collections/comments/save + data={_id: PARENTS_ITEM_ID*, commentsLink: [UPDATED_COLLECTIONLINK_DATA_ARRAY]} 
*) having the _id key set in a collections-save call triggers an “update” for which it is not necessary to post the whole object but is sufficient to only post the to-be-updated fields