Burkina Faso international Kabore spent last season on loan with Wrexham but made his move from Manchester City permanent in the summer.
He returned to the Racecourse Ground on the eve of the contest with Birmingham, signing a three-year deal with the north Wales side.
The 25-year-old has featured 10 times in the Championship so far this season.
O’Hare also put pen to paper on a three-year contract with Wrexham in the summer after opting to leave Sheffield United.
Wrexham – currently 17th in the second tier after 12 games – are understood to be actively improving measures at the club to avoid future issues.
They are thought to be hiring a club secretary in addition to improving administrative training.
A club official told BBC Sport Wales that the incidents involving Kabore and O’Hare were no fault of boss Phil Parkinson, the club’s coaching staff or new sporting director Steve Nickson – who was not officially appointed to his role until 7 September.
The Wrexham statement added: “The club is taking the appropriate steps to prevent such issues occurring in the future.”