Record name in traditional stories from the east (5)
I believe the answer is:
enrol
'record' is the definition.
(I know that enrol is a type of register)
'name in traditional stories from the east' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'in' means one lot of letters goes inside another.
'traditional stories' becomes 'lore' (lore is tradition or learning).
'from the east' says the letters should be written in reverse (on a map from right to left).
'n' going into 'lore' is 'lorne'.
'lorne' written backwards gives 'ENROL'.
(Other definitions for enrol that I've seen before include "Sign up (member)" , "Register officially" , "Recruit" , "Become a member" , "Loner (anag.)" .)