Stick used by extremely brittle Muslim prince’s widow (5)
I believe the answer is:
begum
'muslim prince's widow' is the definition.
'stick used by extremely brittle' is the wordplay.
'stick' becomes 'gum' (I've seen this before).
'used by' means one lot of letters go next to another.
'extremely' means to remove the middle letters.
'brittle' with its middle removed is 'be'.
'gum' put after 'be' is 'BEGUM'.
(Other definitions for begum that I've seen before include "High-ranking Muslim woman" , "She's high-ranking" , "Muslim lady" , "Muslim princess" , "Moslem princess" .)