You can try this:
````
Calculated Column DEPT:

=IF((DateRequest<=TODAY()+7),"DepA",IF(AND(DateRequest>(TODAY()+7),DateRequest<=Expire),"DepB","DepC"))

````
Note: Since ````[Expire]```` is based on ````[Created]```` date, I would replace ````TODAY()```` with ````[Created]```` for this formula as well, otherwise ````DEPT```` value will change if any column value is changed.


[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/iHc8U.png