UTC is counted with atomic clocks. The Earth's rotation is slightly irregular, so UTC is occasionally adjusted by one leap second, announced in advance by the International Earth Rotation and Reference Systems Service. The second is inserted at 23:59:60 UTC, usually on 30 June or 31 December.
Local clocks that follow a time zone take the same UTC adjustment. You do not add a leap second on top of a daylight-saving change. Everyday timers on this site count SI seconds on the device clock. They do not predict a future leap second, because none is scheduled until the observatories announce one.