Inadequacy of paintings he had put up outside (6)
I believe the answer is:
dearth
'inadequacy' is the definition.
(dearth is a kind of inadequacy)
'paintings he had put up outside' is the wordplay.
'paintings' becomes 'art' (I've seen this before).
'he had' becomes 'hed'.
'put up' says the letters should be written backwards.
'outside' indicates putting letters inside.
'hed' back-to-front is 'deh'.
'art' put inside 'deh' is 'DEARTH'.
'of' acts as a link.
(Other definitions for dearth that I've seen before include "Acute shortage" , "Scarcity - famine" , "Severe lack" , "want" , "Lack of resources" .)