Appeal Court judges decided last week to reduce her term by one week, after she claimed she would not be allowed to visit her sons or grandchildren in New Zealand.
Legislation restricts anyone who has been convicted and sentenced to imprisonment for 12 months or more in the last 10 years from coming to New Zealand.
A spokeswoman for Immigration New Zealand said visa applicants had to prove they were of good character.
"A conviction which has resulted in a sentence of less than 12 months may also result in a visa application being declined," the spokeswoman said.
Clayton's barrister told the court she was "deeply sorry" for her crime and intended to pay back all of the money by selling her house.
Her job with the council was organising events for young people. She would book acts and companies, some of which were paid in cash.
Between 2005 and 2010, Clayton deposited the stolen funds into her bank account, inventing fictitious companies, submitting false invoices or inflating genuine invoices, and keeping the difference to try to hide her theft.
She was discovered after an internal council audit in 2010 and was arrested in January last year, the Melton Times said.
The court heard she was "in dire straits" after a relationship break-up and was suffering from chronic fatigue and stress when she stole the money.
Clayton had been caring for her former partner who had been diagnosed with multiple sclerosis and dementia.
She planned to move to New Zealand because she had no family left in the United Kingdom, the Melton Times said.
Allowing the appeal, Lady Justice Hallett said: "We are persuaded the consequences for this appellant, her sons and her grandchildren, of her not even being able to visit them in New Zealand would be far-reaching and long-standing and, in that sense, could be described as excessive."
