The phrase "next available time" is correct and usable in written English.
You can use it when you are referring to the first time after the present when a given activity can be performed. For example, "I will call you at the next available time."
The next available time will be at Closing Ceremony II, in November.
It's best to call Ms. Traci Miller at 609-258-4554, and she will make an appointment at the next available time.
The source will schedule the packet directly, so the backoff time, T back, in this case is the next available time instant.
Fortunately, while we were still in line, a museum worker was able to reassure us that we could attend at the next available time, despite having missed our reservation time.
Nine studies reported the proportion of participants meeting recommended levels of physical activity at baseline and 12 months (or at the next available time point, if 12 month data were not available).
If I had stayed in New York, I'd have started a dozen major tasks reserved for the next available 'down time'.
Since users generally don't have to schedule in advance anymore, the app pre-fills the order screen with a customer's default address and the next available pickup time.
The on-call nurse from the Nephrology Unit opened the next available envelope each time a patient was enrolled in the study.
Students typically wait 10 minutes for the next available counselor; however wait times vary depending on the volume of students seeking drop-in services.
A few minutes afterward, Bruce called back to say that the next available flight was in three days' time.
According to The Fuqua CMC Recruiting Policies, if the CMC does not receive the closed list or an update from the recruiting partner by the due date, the sector manager may reschedule the company's campus interview for the next available date to allow the extra time needed to decide on closed list candidates.
