Dad's mid-century history (4)
I believe the answer is:
past
'history' is the definition.
(I've seen this before)
'dad's mid-century' is the wordplay.
'dad's' becomes 'pa's' (both can mean one's father).
'mid' indicates the central letters (mid- can mean the middle of something).
The middle letter of 'century' is 't'.
'pas'+'t'='PAST'
(Other definitions for past that I've seen before include "A person's earlier life history" , "Beyond" , "Ended" , "over and done with" , "Finished, gone" .)