The visiting side secured an emphatic 7-0 victory over Cheltenham Town in their cup curtain-raiser two weeks ago and will be looking to continue in the same vein.
Match preview
Gillingham failed to find their feet in the new League Two campaign as they were held to an uneventful goalless draw by Walsall in front of their home crowd on Saturday.
In a drab contest in South East England, the Gills were made to pay for their lethargic display in front of goal, where they were guilty of a lack of sting, before settling for a share of the spoils.
Prior to that, Neil Harris's men were on a run of two consecutive defeats, losing 3-0 at Tranmere Rovers on August 13 before suffering a 2-0 home defeat at the hands of Harrogate Town three days later.
Gillingham now turn their attention to the EFL Cup, where they kicked off their campaign with a 2-0 victory away to AFC Wimbledon two weeks ago, with Mikael Mandron and Jordan Green finding the target in injury time.
Tuesday's hosts will be looking to arrest their slump and surpass their 2021-22 cup run, where they were sent packing in the second round courtesy of a penalty shoot-out loss to Cheltenham Town.
Exeter City, on the other hand, were denied a third consecutive home victory in the League One on Saturday, when they fell to a 1-0 against Cheltenham Town at St James Park.
Off the back of a 3-1 victory over Wycombe Wanderers, the Grecians failed to pick up where they dropped off as Southampton loanee Dan N'Lundulu scored the only goal of the game to hand the visitors their first win of the season.
However, with an emphatic 7-0 victory over Cheltenham Town in the EFL Cup opener still fresh in their minds, Exeter City will head into Tuesday full on confidence as they look to return to winning ways.
While Matt Taylor's men have managed just one win in their last five competitive games away from home, they will fancy their chances against a Gillingham side who have failed to taste victory in each of the last four meetings between the sides since 2009.
Gillingham EFL Cup form:
Gillingham form (all competitions):
Exeter City EFL Cup form:
Exeter City form (all competitions):
Team News
Gillingham will be without the experience of 35-year-old midfielder Shaun Williams, who is set to miss his second consecutive game after coming off injured against Tranmere Rovers on August 13.
He is joined on the Gills' injury table by newly-signed Australian goalkeeper Ashley Maynard-Brewer, who is yet to make his debut after picking up an injury back in January.
Meanwhile, Dom Jefferie could be involved in the matchday squad for the first time in six games as he pushes to be fit after sustaining an injury in the league curtain-raiser against AFC Wimbledon on July 30.
As for Exeter City, Jevani Brown, who has registered three goals and two assists in the opening four League One games, will play no part in Tuesday's contest after being called up to the Jamaican national team.
On the injury front, Taylor will be unable to call upon the services of 22-year-old English midfielder Kyle Taylor, who has been sidelined since March's 2-0 victory at Oldham Athletic.
Gillingham possible starting lineup:
Morris; Wright, Ehmer, Baggott; Alexander, Reeves, O'Keefe, Law; Adelakun, Mandron, Green
Exeter City possible starting lineup:
Blackman; Diabate, Stubbs, Hartridge; Caprice, Sparkes, Collins, Kite, Dieng; Nombe, Jay
We say: Gillingham 1-2 Exeter City
While Exeter City have struggled to put together a fine run of form, they head into Tuesday's contest as slight favourites. They are unbeaten in four consecutive games against the Gills and we predict they will extend their recent dominance in the history of this fixture.