Ignoring the odds, Arsenal limp to dominion (5)
I believe the answer is:
realm
'dominion' is the definition.
(I've seen this before)
'ignoring the odds arsenal limp' is the wordplay.
'ignoring the odds' means one should take alternating letters (letters in odd-numbered positions are removed).
'arsenal'+'limp'='arsenallimp'
The alternating letters of 'arsenallimp' are 'REALM'.
'to' acts as a link.
(Other definitions for realm that I've seen before include "region" , "Land under a king or queen" , "field of study" , "King's domain" , "monarch's responsibility" .)