Publication of chart upset extremely posh half of hamlet (8)
I believe the answer is:
pamphlet
'publication' is the definition.
(pamphlet is a kind of publication)
'chart upset extremely posh half of hamlet' is the wordplay.
'chart' becomes 'map' ('map' can be a synonym of 'chart'**).
'upset' says the letters should be written in reverse.
'extremely' suggests removing the centre.
'half of' suggests halving the letters.
'posh' with its centre removed is 'ph'.
'map' back-to-front is 'pam'.
'hamlet' with half the letters taken is 'let'.
'pam'+'ph'+'let'='PAMPHLET'
'of' is the link.
(Other definitions for pamphlet that I've seen before include "Leaflet containing information" , "Small book" , "Brochure" , "Flier" , "Small booklet of information" .)