Doctrine briefly troubles one member of Muslim sect (7)
I believe the answer is:
ismaili
'member of muslim sect' is the definition.
The definition suggests a singular noun which matches the answer.
'doctrine briefly troubles one' is the wordplay.
'doctrine' becomes 'ism' (suffix for disciplines or schools of thought).
'briefly' means to remove the last letter.
'troubles' becomes 'ails' (as verb).
'one' becomes 'i' (Roman numeral).
'ails' with its final letter taken off is 'ail'.
'ism'+'ail'+'i'='ISMAILI'
Can you help me to learn more?
(Other definitions for ismaili that I've seen before include "from a religious sect" , "Aga Khan follower" , "Muslim sectarian" , "One of a Shiite sect" , "Shiite sect member" .)