Little time to publish flimsy paper (6)
I believe the answer is:
tissue
'flimsy paper' is the definition.
(I've seen this before)
'little time to publish' is the wordplay.
'little time' becomes 't' (abbreviation for time).
'to publish' becomes 'issue' ('issue' can be a synonym of 'publish').
't'+'issue'='TISSUE'
(Other definitions for tissue that I've seen before include "Cells sharing a function" , "Disposable handkerchief" , "Bodily matter" , "load of lies?" , "cellular network" .)