Terrible place — greeting cut short (4)
I believe the answer is:
hell
'terrible place' is the definition.
'hell' can be an answer for 'place' (I have seen 'Infernal place' mean 'hell' so perhaps 'place' could also mean 'hell'). I am unsure of the 'terrible' bit.
'greeting cut short' is the wordplay.
'greeting' becomes 'hello' (hello is a kind of greeting).
'cut short' means to remove the last letter.
'hello' with its final letter taken away is 'HELL'.
Can you help me to learn more?
(Other definitions for hell that I've seen before include "uproar" , "Abode of evil spirits" , "Realm of eternal suffering" , "'The road to . . . . is paved with good intentions'" , "One of spelt out words" .)