Old duke, surprisingly, not originally known to sweat (5)
I believe the answer is:
exude
'to sweat' is the definition.
(I've seen this before)
'old duke surprisingly not originally known' is the wordplay.
I cannot quite understand how this works, but
'old' could be 'ex' (prefix meaning former or onetime) and 'ex' is found within the answer.
'duke' could be 'd' (abbreviation) and 'd' is found in the answer.
This explanation may well be incorrect...
(Other definitions for exude that I've seen before include "Discharge (eg, moisture)" , "Show, say, confidence - ooze out" , "Discharge by sweating" , "Be slowly discharged" , "Secrete" .)