The phrase "available slots" refers to the open or free spaces, opportunities, or time periods that can be filled or used for a particular purpose. Full definition
If the company is hiring immediately, it goes without saying that you should take the first available slot. (cvresumewritingservices.org)
Because the school tours were being offered free, in an area where most children had very little prior exposure to cultural institutions, demand for visits far exceeded available slots. (nytimes.com)
I did inquire about spa appointments but the earliest available slot would have been after I had to be at the gate. (frequentbusinesstraveler.com)