Starts to seem highly engrossed by Eastern faith (6)
I believe the answer is:
shinto
'eastern faith' is the definition.
(I've seen this in another clue)
'starts to seem highly engrossed by' is the wordplay.
'starts to' indicates taking the first letters.
'engrossed by' becomes 'into' (I've seen this in another clue).
The first letters of 'seem highly' is 'sh'.
'sh'+'into'='SHINTO'
(Other definitions for shinto that I've seen before include "Ancestor-worshipping religion of Japan" , "State religion of Japan until 1945" , "Japanese worship" , "Japanese cult" , "faith" .)