back up macbook air- not enough space

Hi

I have a problem with my backup

I am trying to back up my macbook air with time machine to external hard drive

I had did one backup with these device and iall went good but now to want to do a new backup the time machine failed all the time and it says I don't have room, which is true as I saw' but t thought that when it backup it do it on the old backup

I tried to delete the old back but didn't work

if somebody know how to help with this issue?