The phrase "but on one condition" is grammatically correct and commonly used in written English.
It is usually used to introduce a limiting factor or requirement in a statement. Here is an example: "I will go to the party with you, but on one condition – I can leave early if I start feeling unwell."
He is likened to the Bald Man in an Albanian folktale, who is rescued from Hell by an eagle—"but on one condition.
A conditional hospitality and unconditional hospitality must remain inseparable, self-prescribe, but on one condition: that we can think and machine and Event compatible as two inseparable concepts.
But on one condition -- that this time Turkey get real.
We fully respect the principle of self-regulation, but on one condition: that good governance is guaranteed".
See if you can do it, but on one condition: not at the expense of the boys".
Hades grants his request, but on one condition: as he leaves the Underworld, with her following in his footsteps, he must not look back.
Mr. Maxwell described the moment: "He said you have some skills, and I'll train you on one condition, that you give up everything and focus on boxing.
In this case, he was willing to take that risk, but only on one condition, he said: that any mention of his dining habits also include a word about his little-known profession.
At first Jurist-Rosner and Roche were advised to focus on one condition only, but they realized that would be very difficult because many health issues exist simultaneously and must be treated at the same time.
Mr. Gewanter said he did not know the identity of the whistleblower but said he or she had insisted on one condition: that any newspaper wishing to use the information had to expose members of all political parties.
The Black Panthers' minister of information, Eldridge Cleaver, was in jail, but, from his cell, gave Life the go-ahead on one condition.
