"a mutually agreed time" is correct and usable in written English.
You can use it to refer to a time that is set and agreed upon by two or more people. For example: "We set a mutually agreed time to meet at the park."
Transfer and extubation should adhere to a mutually agreed time line.
On recruitment, participants will be required to attend an initial laboratory session with the experimenter at a mutually agreed time.
The one-to-one session will be scheduled at a mutually agreed time, will be conducted by telephone and should last about 15 30 minutes.
Within 72 h of initial screening and allocation to the intervention, the assigned Compassionate Communities Volunteer visits the person at a mutually agreed time, in the person's own home, to identify their social and practical needs and the type of support required.
Patients are contacted via telephone by the specialist nurse at mutually agreed times.
If a woman cannot be interviewed at the time of contact, a mutually agreed upon time and place will be scheduled for another visit and interview.
If the woman cannot be interviewed at the time of contact, a mutually agreed upon time and place will be scheduled for another visit and interview.
The Data Coordinator/Monitor will conduct site visits four times annually at a mutually agreed upon time for the purpose of auditing the study.
Upon first phone contact with the nurse, a mutually agreed upon interview time and place was established and the nurse traveled to a given interview site at the appointed time.
In May 2003, the United Kingdom and South African governments signed a MoU to "give cognisance to the existing commitment of the United Kingdom to ethical international workforce policies and practices……South African health personnel can spend a mutually agreed period of time on education and practice in organizations providing National Health Services" [ 22].
Better to know this ahead of time, so you can plan a mutually agreed upon budget.
