Earl lives extravagantly, acquiring second chateau (10)
I believe the answer is:
versailles
'chateau' is the definition.
(Chateau de Versailles is a French palace)
'earl lives extravagantly acquiring second' is the wordplay.
'extravagantly' is an anagram indicator (I've seen this in other clues).
'acquiring' means one lot of letters goes inside another.
'second' becomes 's' (common abbreviation).
'earl'+'lives'='earllives'
'earllives' anagrammed gives 'verailles'.
'verailles' placed around 's' is 'VERSAILLES'.
(Other definitions for versailles that I've seen before include "Royal Court" , "Palace built by Louis XIV" , "Louis XIV's palace; WW one treaty" , "Palace near Paris" , "French palace" .)