Papers I notice left uncovered, that's foolish (7)
I believe the answer is:
idiotic
'foolish' is the definition.
(I've seen this in another clue)
'papers i notice left uncovered' is the wordplay.
'papers' becomes 'id' (identifying documents are one's 'papers').
'left uncovered' indicates the central letters (letters that cover the word up are removed).
The centre of 'notice' is 'otic'.
'id'+'i'+'otic'='IDIOTIC'
'that's' acts as a link.
(Other definitions for idiotic that I've seen before include "Mindless" , "Half witted" , "Daft" , "Absurd, crackbrained" , "description of Dostoevsky hero?" .)