Great period of austerity following number-crunching program (9)
I believe the answer is:
excellent
'great' is the definition.
(I've seen this before)
'period of austerity following number-crunching program' is the wordplay.
'period of austerity' becomes 'lent' (Lent is a period of self-denial in Christianity).
'following' says to put letters next to each other.
'number-crunching program' becomes 'excel' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'lent' put after 'excel' is 'EXCELLENT'.
Can you help me to learn more?
(Other definitions for excellent that I've seen before include "'Superior, first class (9)'" , "Fine" , "brilliant" , "Quite splendid, extremely good" , "A one" .)