Rent airbase out? That's a puzzle (5,6)
I believe the answer is:
brain teaser
'that's a puzzle' is the definition.
(I've seen this before)
'rent airbase out?' is the wordplay.
'out?' is an anagram indicator (out can mean wrong or inaccurate).
'rent'+'airbase'='rentairbase'
'rentairbase' is an anagram of 'BRAIN-TEASER'.
(Other definitions for brain teaser that I've seen before include "puzzle" , "tricky problem" , "dilemma" .)