Auction last of them in state capital (5)
I believe the answer is:
salem
'state capital' is the definition.
(state capital of Oregon)
'auction last of them' is the wordplay.
'auction' becomes 'sale' (I've seen this in other clues).
'last of' says to take the final letters.
The last letter of 'them' is 'm'.
'sale'+'m'='SALEM'
'in' is the link.
(Other definitions for salem that I've seen before include "holy city" , "US city" , "American capital" , "trial scene" , "where possessions were claimed?" .)