Dispatched exhausted, having lost power (4)
I believe the answer is:
sent
'dispatched' is the definition.
(I've seen this before)
'exhausted having lost power' is the wordplay.
'exhausted' becomes 'spent' ('spent' can be a synonym of 'exhausted').
'having lost' indicates named letters should be taken away.
'power' becomes 'p'.
'spent' with 'p' removed is 'SENT'.
(Other definitions for sent that I've seen before include "charged with emotion?" , "Transmitted" , "Posted" , "Told to go - enthralled" , "Thrilled" .)