Your sentence makes no sense. "If it were not" is subjunctive. It sets up a hypothetical.
Try: "John’s plan to become the team-leader would be succeeding, if it were not for other promises made by management."
Student or Learner
Johnís plan to become the team-leader was succeeding so far, if it were not for other promises the management would make.
- What does the bold part exactly mean? Can I omit the word "for" and say, "if it were not other promises...."?
If you want to omit something, you can omit if and say were it not for other promises.... (Note the inversion)
Also, I would not use the comma after succeeding.