Member of old empire in La Paz must be optimistic, finally (5)
I believe the answer is:
aztec
'member of old empire' is the definition.
(someone from the Aztec Empire)
'la paz must be optimistic finally' is the wordplay.
'finally' says to take the final letters.
The final letters of 'la paz must be optimistic' are 'AZTEC'.
'in' is the link.
(Other definitions for aztec that I've seen before include "old American" , "Native of old Mexico" , "Language once used" , "Member of ancient Mexican tribe" , "certain old people" .)