CipSoft said that the new elemental arrows won't replace Diamond Arrows, it only offers some options to hunt in places where creatures are immune or strong to Physical damage and Diamond Arrows can't be used.
A clear example of use:
Froststorm Arrow (Ice Damage) on Gazer Spectres.
They receive only 15% Physical damage and are 130% weak to Ice damage.

The Froststorm Arrow will be much more effective on this creature than Diamond Arrow (130% X 15%).
In all other scenarios where the creature's resistance against Physical is not so high (95%+), or the creature is either neutral (100%) or weak (101%+), Diamond Arrows will always be the best option. It all depends on the creature's elemental sensitivity when considering what is better.
It is important to note that Diamond Arrows have 16 more attack damage than the new elemental arrows, so in many cases this difference will make a better impact on hunts.
There are also some hunts where the arrows will need to be tested to see which option performs better.