Currently there does not seem to be an api Jira Software Cloud REST API to get the priority sequence.
There is one to get all prior /rest/api/3/priority
and specific priority /rest/api/3/priority/2
Is there a way to get the priority sequence/order eg: which is Highest → High → Med → Low so on…
This is interesting. I checked it out and played around by moving the priority order in my settings, and also added new priorities; what I noticed is the list being returned by Get Priorities is already in order. I have not seen an official documentation that says this behavior (maybe Atlassian folks can help us confirm this, tagging @aagrawal2 / @dmorrow ), but it does seem that the returned list is in descending order with the 1st item being the highest priority.
Please try it out and see if that works for your use case.
I looked at the code and the returned list is in descending order of priority. i.e. the highest priority is first.
I have created ACJIRA-2316 to have the documentation improved.