Jobs for teachers tend to come up at certain times of the year. They will usually be announced if somebody is leaving, which means they have already found a new teaching job themselves. This means that it will often be around the end of the spring term when positions start to become available. If you want a new job sooner than that, it can be a little trickier to find one.
Many schools do still need teachers, however – there just might not be quite as many opportunities. You may find that they want to hire teachers on a temporary basis to meet their needs in the most flexible way – they will also know it is harder to find new teachers at more unusual times of the year. You might want to consider supply teaching to find more flexible opportunities outside of the peak times and to find opportunities at times that are relevant to you.