Hunter hired Tulchan as his initial £200m takeover offer - made via bidding vehicle West Coast Capital - was rejected for being too low.
Tulchan founder and ex-Brunswick partner Andrew Grant leads the brief.
The work largely involves strategic media relations work.
Hunter - a well-known associate of Bhs chief Philip Green, who bought Arcadia for £850m in September - is understood to be planning to take HoF private and invest in the stores over a three-to-five year period.
There has been widespread speculation that Green and Hunter are attempting to dominate the reshaping of the UK high street, but Grant said Green has 'nothing to do with' the HoF bid.
Tulchan works opposite HoF's retained financial agency Brunswick, which was hired two months ago (PRWeek, 25 November).
- Brunswick has been hired to handle international media relations for French bank BNP Paribas, which is battling to buy its smaller rival Credit Lyonnais.
BNP recently won a 10.9 per cent stake in Lyonnais after a state auction, then bought a further 5.3 per cent to boost its share.
It is thought Credit Agricole is also still interested in acquiring Lyonnais.