Cautious, cleaner close to canary (5)
I believe the answer is:
chary
'cautious' is the definition.
('chary' can be similar in meaning to 'cautious')
'cleaner close to canary' is the wordplay.
'cleaner' becomes 'char' (charwoman is a type of cleaner).
'close to' indicates one should take the final letters (the close/ending of).
The last letter of 'canary' is 'y'.
'char'+'y'='CHARY'
(Other definitions for chary that I've seen before include "Cautious, wary" , "Cautiously reluctant" , "Circumspect" , "Careful" , "cagy" .)