Slater would say use local openers first (9)
I believe the answer is:
woodlouse
'slater' is the definition.
(synonyms)
'would say use local openers first' is the wordplay.
'say' shows a homophone (sound like).
'use' becomes 'ouse' (I can't explain this - if you can you should believe this answer much more).
'openers' suggests taking the first letters.
'first' says to put letters next to each other.
The first letter of 'local' is 'l'.
'would' sounds like 'wood'.
'ouse' put after 'l' is 'louse'.
'wood'+'louse'='WOODLOUSE'
Can you help me to learn more?
(Another definition for woodlouse that I've seen is " Damp-loving creepy-crawly".)