The order of the items in a linked record field can be manually reordered or reversed with a toggle.
Reverse order toggle
A linked record may have a toggle "Show linked records in reverse order" in your base if it was created before April 2020. This toggle allows you to change the direction of the existing items in the cell and also affects the order of newly added items.
When the toggle is on (legacy behavior), any new linked record you select will be added to the beginning of the list. The default for new linked record fields is for the toggle to be off so that items are listed in the order they are added to the cell.
This option to toggle this legacy behavior will only be available on older bases created when this was the default such as in many of the templates in our template gallery and Airtable Universe. Once you untoggle this option on all attachment and linked record fields in the base, the option to show the items in reverse order will no longer display.
You can reorder record links by expanding a cell within a linked record field, and clicking and dragging the links.