We don't have synonyms for woolsack yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are woolpack, coalsack and woolstock.
(n) :
A seat made of wool; (specifically) the traditional seat of the British Lord Chancellor (since 2006 of the Lord Speaker of the House of Lords); hence (by metonymy) the post of Lord-Chancellor.
(n) :
A seat made of wool; (specifically) the traditional seat of the British Lord Chancellor (since 2006 of the Lord Speaker of the House of Lords); hence (by metonymy) the post of Lord-Chancellor.