Gloucestershire 240 (van Buuren 83, Noema-Barnett 73*, Henry 6-58) and 73 for 0 trail Kent 582 for 9 dec (Denly 107, Stevens 89, Rouse 55, Podmore 53*, Miles 4-122) by 269 runs
Sam Billings is in danger of becoming a captain without portfolio, observing from afar while Kent make impressive progress towards possible County Championship promotion.
Since he succeeded Sam Northeast as captain, Billings has played just four Royal London Cup matches for Kent and has yet to feature in their Championship campaign.
Billings opted to start the season with Chennai Super Kings in the IPL rather than Kent and is now away on international duty with England. If he remains in England's ODI and T20 squads, it could be another month before Kent see their captain again.
But Billings' international future is far from assured. Since he made 56 against Kolkata Knight Riders on April 10, Billings has scraped just 78 in runs in his last 12 innings - 10 of them in three innings for Kent. His latest failure came in England's embarrassing defeat by Scotland on Sunday when he slapped a full toss to midwicket.
In Billings' absence, Adam Rouse has performed admirably behind the stumps and vice-captain Joe Denly has led the side to three successive Championship wins. A fourth, which would avenge an opening-round defeat by Gloucestershire at Canterbury, is possible here against a side that has struggled to match the intensity of Kent's cricket over the first three days.
Despite Billings' absences and lack of runs, it seems certain that Rouse will make way the next time the captain becomes available for county duty with Kent placing faith in Billings' leadership qualities and historic performances with the bat.
"Off the field, Sam has been unbelievable," Kent assistant coach Allan Donald said. "There is nothing we can do about his England commitments because everyone wants to play international cricket. When he comes back someone has to make space, it's as simple as that.
"Sam is a world-class cricketer. I have been very impressed with the way he captains the team especially his aura in the dressing room and the way he speaks to the players. He is very impressive. He hasn't burnt the house down at the moment in terms of runs but he will come good, there is no question about it."
Kent seem to be doing very nicely without Billings thanks largely to the outstanding contribution of Matt Henry, the New Zealand pace bowler, who has taken 43 of their 85 Championship wickets so far.
Henry will be available for the top-of-the-table clash against Warwickshire at Tunbridge Wells next week and the day-night match against Middlesex at Canterbury before he returns home. Kent are already trying to persuade New Zealand to allow Henry to return for their last five Championship matches, including a potential Division Two title decider against Warwickshire at Edgbaston.
"Matt has brought leadership, he's brought skill and great intensity to this group which is what you want from a guy who has played international cricket," Donald said.
Donald displayed similar qualities during a long and distinguished career as Warwickshire's overseas player and the former South Africa fast bowler watched admiringly as Henry overcame a slow, low and used pitch with skill and aggression.
Henry, who claimed his fourth five-wicket haul of the season, took three for nine in 27 balls with the second new ball and needed only two deliveries with it to break an obdurate seventh-wicket partnership of 104 between Graeme van Buuren and Kieran Noema-Barnett.
Chris Dent and Benny Howell applied themselves better when Gloucestershire followed on 342 in arrears and Kent suffered a setback when Harry Podmore crumpled in his delivery stride clutching his right knee and was helped off the field by Donald.