Brief period in deficit (8)
I believe the answer is:
shortage
'deficit' is the definition.
(I know that deficit can be written as shortage)
'brief period' is the wordplay.
'brief' becomes 'short' (synonyms).
'period' becomes 'age' (age is a kind of period).
'short'+'age'='SHORTAGE'
'in' is the link.
(Other definitions for shortage that I've seen before include "Horse tag (anag.)" , "Deficit" , "famine" , "Insufficiency" , "Her goats (anag)" .)