Odds on royal princess opening bridge (7)
I believe the answer is:
spanner
'bridge' is the definition.
(something which spans two points)
'odds on royal princess opening' is the wordplay.
'odds' becomes 'sp' (betting abbreviation for starting price).
'on' is a charade indicator (letters next to each other).
'royal' becomes 'r' (abbreviation).
'princess' becomes 'anne' (Princess Anne, daughter of Queen Elizabeth).
'opening' indicates putting letters inside (some letters open a gap in others).
'sp'+'r'='spr'
'spr' placed around 'anne' is 'SPANNER'.
(Other definitions for spanner that I've seen before include "Tool, often adjustable" , "Nut turner" , "In the works, this tool is a headache" , "that might cause difficulty in the works" , "Tool for tightening or loosening" .)