Curtailed a long period of deficiency (8)
I believe the answer is:
shortage
'deficiency' is the definition.
(shortage is a kind of deficiency)
'curtailed a long period' is the wordplay.
'curtailed' becomes 'short' (similar in meaning).
'a long period' becomes 'age' (I've seen this in another clue).
'short'+'age'='SHORTAGE'
'of' acts as a link.
(Other definitions for shortage that I've seen before include "Horse tag (anag.)" , "may put price up" , "Her goats (anag)" , "Dearth, lack" , "famine" .)