Mr Alexander announced on Friday he has successfully renounced his UK citizenship ties,clearing the way to seek re-election.
The 67-year old is favoured to retain the seat based on his personal popularity and past conservative voting patterns.
But the former backbencher faces a ferocious campaign from Labor,which hopes to turn the byelection into a referendum on the performance of the federal government. With a one-seat majority in the House of Representatives,the Bennelong race could determine whether the embattled Coalition retains its position or is forced to rely on crossbenchers for confidence and supply.
Adding to the risk is the potential for a slew of other byelections in early 2018 as new dual citizen cases are identified in the House of Representatives.