The history of dad’s East End (4)
I believe the answer is:
past
'the history' is the definition.
(I've seen this before)
'dad's east end' is the wordplay.
'dad's' becomes 'pas' ('pa' can be a synonym of 'dad').
'end' indicates one should take the final letters.
The last letter of 'east' is 't'.
'pas'+'t'='PAST'
'of' is the link.
(Other definitions for past that I've seen before include "A person's earlier life history" , "Bygone" , "Beyond" , "tense" , "Days gone by" .)