Transaction log backup I have database of 800GB average but when I run a backup job (of system and user databases) the transaction log backup reports a failure: There is not enough space on the disk.

When I make a transaction log backup the size of this would decrease or do I need a shrink (after or before run a backup)?
Shrinking is bad for performance and is a waste of time since it's just going to grow again. You need to add more disk space to accommodate the backups that you need. If you don't care about point-in-time recovery for the database, which it sounds like may be the case since there isn't enough storage even for a LOG backup, switch your recovery model to SIMPLE. With SIMPLE, you won't need LOG backups. But which recovery model you need is dependent upon your business needs of the database.