Man turned up with sentry, polishing off the odd half (6)
I believe the answer is:
moiety
'half' is the definition.
(moiety is a kind of half)
'man turned up with sentry polishing off the odd' is the wordplay.
'man' becomes 'iom' (Abbreviation for the Isle of Man).
'turned up' says the letters should be written in reverse.
'with' means one lot of letters go next to another.
'polishing off the odd' means one should take alternating letters (letters in odd-numbered positions removed).
The alternate letters of 'sentry' are 'ety'.
'iom' written backwards gives 'moi'.
'moi'+'ety'='MOIETY'
(Other definitions for moiety that I've seen before include "Part" , "Oy! Time for a half" , "Either of two" , "Fair portion" , "A legal sort of half" .)