A small amount, say 1,000 — signed off (7)
I believe the answer is:
smidgen
'a small amount' is the definition.
(I've seen this in another clue)
'1000 signed off' is the wordplay.
'1000' becomes 'M' (synonyms).
'off' indicates anagramming the letters.
'm'+'signed'='msigned'
'msigned' is an anagram of 'SMIDGEN'.
'say' is the link.
(Other definitions for smidgen that I've seen before include "bit!" , "Scarcely detectable amount" , "A very small amount (7)." , "Tiny part" , "Iota" .)