Bow to oligarch, halfway (4)
I believe the answer is:
arch
'bow' is the definition.
(both can mean to curve)
'oligarch halfway' is the wordplay.
'halfway' indicates taking half.
'oligarch' with half the letters taken is 'ARCH'.
'to' acts as a link.
(Other definitions for arch that I've seen before include "Embow" , "Construction with a keystone" , "Curved span" , "Cunning; bridge" , "Prefix meaning chief - maybe an angel" .)