This mainly depends on the current selected view
and the current toolbar type
In case,
- The
selected view
is Summary view
,
- The
toolbar type
is summary toolbar
or any other type else No toolbar
You will get the old add new
,

Note: after selecting Summary view
, summary toolbar
, you should stop editing the page to get it reflected with the old add new
link.
Unfortunately, when you edit the list view web part
, you can't specify which view is currently selected, and it shows by default Current View
So, it's not a good solution to remove the web part and add it again because you don't know which view was selected!
The recommended workaround to change the selected view
to any other view else Summary view