Piece about small city district cut in half (6)
I believe the answer is:
bisect
'cut in half' is the definition.
(synonyms)
'piece about small city' is the wordplay.
'piece' becomes 'bit' (synonyms).
'about' indicates putting letters inside.
'small' becomes 's' (abbreviation - e.g. clothes size).
'city' becomes 'EC' (the City of London postcode).
's'+'ec'='sec'
'bit' going around 'sec' is 'BISECT'.
'district' is the link.
I am not very happy about this link. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for bisect that I've seen before include "Cut equally in two" , "equally split" , "Halve (angle)" , "create schism?" , "Cut in two equal parts" .)