Shortage female in charge discovered in tight diet (7)
I believe the answer is:
deficit
'shortage' is the definition.
(I've seen this before)
'female in charge discovered in tight diet' is the wordplay.
'female' becomes 'f' (abbreviation).
'in charge' becomes 'ic'.
'discovered in' is an insertion indicator.
'tight' indicates anagramming the letters (tight can mean drunk).
'f'+'ic'='fic'
'diet' anagrammed gives 'deit'.
'fic' put into 'deit' is 'DEFICIT'.
(Other definitions for deficit that I've seen before include "Excess of liabilities over assets" , "There's something lacking" , "Financial shortfall" , "Amount of which total falls short" , "Shortage" .)