He is taken in by a bearded Indian desert chief (6)
I believe the answer is:
sheikh
'desert chief' is the definition.
'sheikh' can be an answer for 'chief' (I've seen this before). I'm not sure about the 'desert' bit.
'he is taken in by a bearded indian' is the wordplay.
'is taken in by' indicates putting letters inside (back).
'a bearded indian' becomes 'sikh' (I've seen this before. I am not sure about the 'bearded' bit.).
'he' put into 'sikh' is 'SHEIKH'.
Can you help me to learn more?
(Other definitions for sheikh that I've seen before include "Head of Arab tribe, village etc" , "Broadcast upset" , "Arab ruler" , "Arab leader or prince" , "Leader of an Arab tribe, a Muslim chief" .)