Engineering graduate having rung to order (7)
I believe the answer is:
bespoke
'to order' is the definition.
'engineering graduate having rung' is the wordplay.
'engineering graduate' becomes 'be' (Bachelor of Engineering).
'having' is a charade indicator (letters next to each other).
'rung' becomes 'spoke' ('spoke' can be a synonym of 'rung').
'be'+'spoke'='BESPOKE'
(Other definitions for bespoke that I've seen before include "Tailor-made" , "Description of tailor" , "Made to measure" , "Custom-made" , "Of clothes, made to order" .)