Again constructs puzzle that's regularly filled in (8)
I believe the answer is:
rebuilds
'again constructs' is the definition.
('builds' can be a synonym for 'constructs' so perhaps 'rebuilds' is OK for 'again constructs')
'puzzle that's regularly filled in' is the wordplay.
'puzzle' becomes 'rebus' (type of visual puzzle).
'that's regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'in' is an insertion indicator.
The alternating letters of 'filled' are 'ild'.
'rebus' enclosing 'ild' is 'REBUILDS'.
(Another definition for rebuilds that I've seen is " Puts back together".)