Bequest being clay construction outside, say (6)
I believe the answer is:
legacy
'bequest' is the definition.
(I know that bequest can be written as legacy)
'clay construction outside say' is the wordplay.
'construction' indicates anagramming the letters (answer constructed from certain letters).
'outside' is an insertion indicator.
'say' becomes 'eg' (both can mean 'for example').
'clay' is an anagram of 'lacy'.
'lacy' placed around 'eg' is 'LEGACY'.
'being' acts as a link.
(Other definitions for legacy that I've seen before include "Like old software" , "A bequest, something left in a will" , "One inherited" , "Bombay since 1995" , "Birthright" .)