Rashest at any rate (9)
I believe the answer is:
leastwise
'at any rate' is the definition.
(synonyms)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for leastwise that I've seen before include "infrequently occurring" , "If nothing else" , "anyway" , "However (US)" , "in Hollywood at any rate" .)