Former Northampton fly-half Hepher has been part of Exeter's coaching team since Baxter took over as director of rugby in 2009, while Hunter moved to Sandy Park in 2013 after a successful spell as England Under-20s head coach.
The pair have been part of the backroom team that helped the Chiefs win two Premiership titles and the 2020 European Champions Cup as they reached six consecutive Premiership finals between 2016 and 2021.
But form has dipped in recent seasons and Hepher was removed as head coach on 20 March and tasked with overseeing the backs and attack strategy until the end of the season before switching to an academy role next term, with Hunter taking over as head coach.
The current campaign reached a nadir at Kingsholm with Exeter conceding 13 tries in a shambolic display.
Hunter, rather than director of rugby Rob Baxter, faced the media afterwards, describing the game as his "lowest point" as a coach.
"In no way at all did we have any foothold in that game - nothing really held up and we gave up momentum so easily," he told BBC Radio Devon.
"Right now it's important that we wear it and recognise that that is not an acceptable level of performance from anybody involved."