NEW MAC VS OLD TIME MACHINE

It sounds like you want to use the new iMac with an older Mac's Time Machine External Hard Disk. If that is the case, if the external HD is older that k4-6 years you should strongly consider replacing it as ALL HD's die and it is wise to replace them periodically so you don't lose anything. You can re-purpose the old Time Machine External Hard Disk for some other non essential task. If you do not want to do that then simply format the old Time Machine External Hard Disk using Disk Utility and start Time Machine all over.

Connecting the TM drive to a new iMac will trigger a full backup which is bigger than the hourly backups the old Mac was making. This may account for the lack of space.