When his true identity was established Rennie was sent a summons to court to face charges but he failed to do so. He was subsequently arrested and refused bail last month.
Rennie's lawyer Whare Hika urged Judge Peter Rollo to keep the jail sentence as short as possible, as his client was on a waiting list for surgery to his arm and nose. Mr Hika said his client was remorseful and accepted prison release conditions requiring him to undergo counselling.
Judge Rollo told Rennie his continued flouting of the law was serious. "While there was not driver's fault involved in these offences, your prior convictions history is significant and a serious aggravating factor."
Judge Rollo also noted that the pre-sentence report revealed Rennie had tried to minimise his offending during the "difficult and truncated" interview he had with the report writer.
The judge said Rennie had initially claimed he was unaware that he was still disqualified from his last two drink-driving convictions in 2009 for which he was sentenced 18 months' prison as well as being indefinitely disqualified.
Rennie had then later stated he thought he would "get away with it" - that is, lying to police.
Judge Rollo said: "Your attitude Mr Rennie to your legal and social responsibilities is appalling.
"I take the view that you are truly a recidivist drink-driver and driver while disqualified, and a prison sentence of 21 months is the appropriate outcome to meet the necessary sentencing principles of denunciation and deterrence."