'Time that was gone', as the middle dropped out (5,3)
I believe the answer is:
stone age
'time that was gone' is the definition.
'stone age' can be an answer for 'time' (I have seen 'Old time' mean 'stone age' so perhaps 'time' could also mean 'stone age'). I'm not sure about the rest of the definition.
'the middle dropped out' is the wordplay.
'the middle' becomes 'stone' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'dropped' becomes 'aged' (ageing is a kind of dropping).
'out' means to remove the last letter.
'aged' with its last letter taken away is 'age'.
'stone'+'age'='STONE-AGE'
'as' is the link.
Can you help me to learn more?
(Other definitions for stone age that I've seen before include "Old time" , "Primitive period" , "time long ago" , "Early period" , "Early epoch when man used pre-metal tools" .)