Carter will leave the role, which he has held since spring 2017, at the end of October.
Hotelplan said his departure was for personal reasons, and wholly unrelated to the coronavirus crisis.
Joe Ponte, managing director of Hotelplan UK subsidiary Explore Worldwide, will formally succeed Carter as Hotelplan UK chief executive on 1 November.
Ponte will also join the Hotelplan Group executive management team, reporting to group chief executive Thomas Stirniman.
Explore deputy managing director John Telfer will take over from Ponte on a temporary basis "until a longer-term successor is found" said Hotelplan in a statement.
Hotelplan acquired adventure specialist Explore in December 2015, with Australian Ponte appointed managing director in June 2018, joining the operator from Flight Centre.
"It has been an absolute privilege to be at the helm here," said Carter. "I have had five challenging but fantastically enjoyable years with our award-winning brands.
"I want to thank my amazing team and colleagues, and the unwavering support from Thomas Stirnimann and the Hotelplan board."
Of Carter, Stirniman said: "I deeply regret Paul’s decision to leave Hotelplan UK, but understand and respect the personal reasons behind this.
"On behalf of the entire executive committee, I would like to offer our sincere thanks for his tireless commitment with the group and wish him the very best for his future".
And of Ponte’s promotion, he added: "I am convinced I have found the ideal successor in Joe Ponte. From his previous role, he knows Hotelplan UK and the current challenges very well. I wish him every success in his new position."
In June, Hotelplan Group announced it would close its office in Godalming, Surrey, and cut more than a quarter of its workforce across its British operators – Inghams, Ski Total, Esprit Ski, Flexiski, Inntravel and Explore.
It was then proposed staff based at Hotelplan’s Godalming office would relocate to Explore’s Farnborough HQ in Hampshire, with staff continuing to work from home – owing to coronavirus – until they can be "safely accommodated" at the new location.
A Hotelplan UK spokesperson confirmed to TTG the plans are still due to go ahead, although have been delayed until the new year owing to the UK’s new Covid guidelines that discourage office working.