Some ancient method showing no particular care (3,3,3)
I believe the answer is:
any old how
'showing no particular care' is the definition.
(in any way or in any order)
'some ancient method' is the wordplay.
'some' becomes 'any' (similar in meaning).
'ancient' becomes 'old' (similar in meaning).
'method' becomes 'how' (I've seen this in another clue).
'any'+'old'+'how'='ANY OLD HOW'
(Other definitions for any old how that I've seen before include "casually" , "Without special care" , "disorderly" .)