Betterton has been at the Government health rationing body since October 1999. She will be away for 12 months.
Ranson will take over the role from next week and will report into the comms director, who has yet to be appointed.
Fish joined Hanover in April as an associate director after seven years at NICE.
Previously, she worked as a consultant at Fishburn Hedges and as a comms officer for the Liberal Democrats.
Fish ran a comms team of 56 at NICE, which is still searching for a replacement for her. Carol Bewick has been brought on board in the interim.
NICE made headlines last week after its ruling that rheumatoid arthritis drug Orencia was 'too expensive'.
Pharma firm Bristol-Myers Squibb had been preparing for the comms challenge since the drug was first rejected last November.