Mendicant's clean clothing stank ultimately (5)
I believe the answer is:
fakir
'mendicant's' is the definition.
(I've seen this before)
'clean clothing stank ultimately' is the wordplay.
'clean' becomes 'fair' ('fair' can be a synonym of 'clean'**).
'clothing' is an insertion indicator.
'ultimately' indicates one should take the final letters.
The last letter of 'stank' is 'k'.
'fair' going around 'k' is 'FAKIR'.
(Other definitions for fakir that I've seen before include "Indian religious ascetic" , "Ascetic in India" , "Holy man of the East" , "Religious mendicant in India" , "Ascetic type" .)