The phrase "after their exit" is correct and usable in written English.
It can be used to refer to events or actions that occur following someone's departure from a place or situation.
Example: "The meeting continued for another hour after their exit, discussing the next steps for the project."
Alternatives: "following their departure" or "subsequent to their exit."
On Monday the Irish, after their exit from the tournament, were not much interested in bottled water.
London Broncos have launched "a full review of the playing department" after their exit from the Challenge Cup last Sunday.
Zlatan Ibrahimovic has admitted he is proud of his Sweden career after their exit from Euro 2016 was confirmed on Wednesday.
After their exit from the first round of the NBA Playoffs in a 7-game thriller against the Los Angeles Clippers last season, the 2014 NBA Champs have started this season in destructive form.
After their exit, they traded away Andre Iguodola in the Dwight Howard megadeal and got back Andrew Bynum, whose injuries turned out to be so severe that there's doubt that he will play a meaningful game in a 76ers uniform.
The former right-back, who also stepped back from his role as an England coach after their exit from Euro 2016, told Sky Sports that he would focus primarily on his business interests for the time being.
Newcastle need to lift themselves quickly as Arsenal did after their European exit.
Five years ago, a leaked photograph of England's footballers having a quiet beer in their South Africa hotel hours after their inglorious exit from the tournament was deemed worthy of the front page of several newspapers.
Valencia's 4-0 defeatoto Zaragoza after their Champions League exit to Schalke last week led the forward Juanma Mata to call on the team to get over their European disappointment quickly.
Cook, who caused a stir this week when he claimed England's decision to replace him as World Cup captain had been proved "probably wrong" after their early exit from the tournament, had the chance to let his bat do the talking.
Celtic, who dropped into the Europa League after their Champions League exit against Maribor, were beaten in a Champions League qualifier by Dinamo Zagreb in 1998.
