More severe in pursuit of each person appearing out of the sunrise (9)

I believe the answer is:
easterner
'person appearing out of the sunrise' is the definition.
I can't tell whether this defines the answer.
'more severe in pursuit of each' is the wordplay.
'more severe' becomes 'sterner' (I've seen this before).
'in pursuit of' means one lot of letters go next to another (some letters chase after others).
'each' becomes 'ea' (abbreviation).
'sterner' after 'ea' is 'EASTERNER'.
Can you help me to learn more?
(Other definitions for easterner that I've seen before include "Resident of Connecticut, perhaps" , "Opposite of westerner" , "Oriental person" , "New Yorker perhaps" , "New Englander, for instance" .)