High-ranking Asian woman say taken in by tramp (5)
I believe the answer is:
begum
'high-ranking asian woman' is the definition.
(term for aristocratic Muslim woman)
'say taken in by tramp' is the wordplay.
'say' becomes 'eg'.
'taken in by' means one lot of letters goes inside another.
'tramp' becomes 'bum' ('bum' can be a synonym of 'tramp').
'eg' placed within 'bum' is 'BEGUM'.
(Other definitions for begum that I've seen before include "High ranking female in India" , "Muslim princess" , "Muslim woman of high rank in India" , "Muslim lady" , "She's high-ranking" .)