Partly open a grate (4)
I believe the answer is:
ajar
'partly open' is the definition.
(as in a door which has been left ajar)
'a grate' is the wordplay.
'grate' becomes 'jar' (both can mean to irritate or annoy).
'a'+'jar'='AJAR'
(Other definitions for ajar that I've seen before include "opened tentatively?" , "Fractionally open" , "Part-open" , "not slammed shut" , "(Door) to, not shut" .)