Term order when saving a new taxonomy term
while I am not aware of a solution that will get you this exactly behavior without spending a bunch of time on a unique setup, there maybe a simple workaround for you to quickly identify the new term and move it to whereever it belongs to.

but first of, the definition or new terms being sorted alphabetically is not entirely true. by default, newly added taxonomy terms have a Weight of '0'.
this Weight value serves as the first sort criteria: terms with a higher Weight value will be further down, as will terms with a lower Weight value (can be negative too) appear further up in the list.
only when multiple terms share the same Weight value, they further get sorted alphabetically.

you can see the exact Weight value for every term by clicking Show row weights just above the top right-hand corner of the table.

so if you have a taxonomy vocabulary where all terms have a Weight of -1 and below, newly added terms will be found at the very bottom of the list.

while this will put new terms to the very end of a list, setting up a list this way may be rather tedious, as you might run out of negative numbers or simply because managing 200+ entries this way can  be a pain in the butt. instead, there is another approach I find myself using most of the time:

there are two View Modes managing Weights: one enables you to manually define a Weight value via a select list (the 'show row weights' mode mentioned above), and the other one lets you sort individual terms via dragging and dropping by clicking on the cross/drag cursor on the very left of each term. when you manually define a term order by dragging and dropping (dont forget to hit Save!), every term will be given a unite Weight value starting by 0.
 this means only the very first term will have a Weight of 0. the second term will have a Weight of 1, the third gets a Weight of 2 and so forth.
when you now add a new term, it will be assigned the weight of 0 as well, placing it as either the very first or second term in the list. this will enable you to find it immediately and place it wherever you need it to be.
if you find yourself wanting to place that new term at the very bottom, dragging it all the way down can be tedious as well, so a quicker way now would be to enable Show row weights again, just pick the lowest value and hit Save.

again, maybe this is not exactly what you are looking for, depending on whether you actually care about the order they are listed, or just want to identify the newest entry.