Hargreaves's last small, advanced spinning jenny (3)
I believe the answer is:
ass
'jenny' is the definition.
(jenny is a female ass)
'hargreaves's last small advanced spinning' is the wordplay.
'last' suggests the final letters.
'small' becomes 's' (abbreviation - e.g. clothes size).
'advanced' becomes 'a'.
'spinning' shows that the letters should be reversed in order.
The last letter of 'hargreaves' is 's'.
's'+'s'+'a'='ssa'
'ssa' in reverse letter order is 'ASS'.
(Other definitions for ass that I've seen before include "A donkey or an idiot" , "Horse hybrid" , "Clinton's behind" , "twit!" , "Silly fellow in passionate state" .)