Select clips in the timeline, right-click and choose 'Scale to Frame Size'.
WARNING: This option entails some consequences in Dynamic Link scenario, not crucial though. You just need to be aware of. In particular, when you replace a clip with a dynamically linked AE composition, and the 'Scale to Frame Size' option had been enabled, After Effects creates a nested precomp out of that clip instead of just a layer, and the Collapse Transformation switch becomes enabled for that precomp in a master comp. If you understand, what all the above is about, take a note. If not, safely ignore until you're facing some issues (e.g. After Effects warning pops up on an attempt to apply the Warp Stabilizer effect etc.)
Okay, thank you for the quick response.
I was hoping, that I could set a hook somewhere und premiere would do this step rightaway,
when I pull the clips to the sequence, as for example final cut does.
As a general rule you should be working in a sequence that matches your footage. You can change it's dimensions upon export.
What other users have motioned is sound wisdom but we do indeed have what your looking for. It's a prefence called 'Default to Frame Size' its under, Prefences> General.
Here's a link to an older toturial showing you how it works.