Thompson, who describes herself as a "board-level communications consultant, writer, and strategist, with private and public sector experience," was headhunted by Unipart last summer.
She left the NHS last month and last week started her new role, overseeing the comms around a new five-year £730m contract Unipart Logistics has with the NHS.
Details of the team she will lead are still to be worked out, since the director of comms role is a new position, Thompson said.
Speaking to PRWeek, she commented: "I’ll report to the managing director for Unipart Logistics and I’ll have a 'dotted line' second report to the director of corporate affairs at Unipart Group."
Thompson said: "One of the reasons why this role is going to be such a good fit is that I’ve spent the last four years in the NHS, but before that I worked in the private sector."
Her experience in the health sector includes more than three years as director of comms at Burton Hospitals NHS Foundation Trust.
Thompson has spent almost 20 years in comms, working in Britain and the US. Previous roles include director of PR at dating app Badoo, corporate comms manager at AOL, head of PR at Zipcar UK, and stints at Lewis PR and Shift Communications.
She remarked that while there are "certain limitations within the public sector", there is more focus on consultations and public engagement.
"I think the private sector could learn a lot from that and could do an awful lot more engagement work so I’m going to try to take that into this role as well."
The Unipart logistics contract has been the subject of controversy.
Failed bidder DHL Supply Chain took the Department of Health and Social Care (DHSC) to court last year, accusing the government department of not conducting the tender process properly. The High Court rejected the claim.
Under the new contract, which started at the end of last month, Unipart is responsible for delivering medical devices and hospital supplies (other than medicine) to NHS trusts, as well as warehousing, inventory management, order-processing and a home delivery service for patients.
Thompson’s job will cover all external and internal comms relating to the contract.
She explained that the main aim is to ensure that "we are doing our very best job to keep people informed and to make sure that the benefits of Unipart’s approach are evidenced to all of our stakeholders."
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