Should I say "this is a new pair of trousers" or "this is a pair of new trousers"?
Maybe native speakers never say it this way?
The natural way is "This is a new pair of trousers". We call the piece of clothing either "a pair of trousers" or just "trousers", so the adjective should come before the piece of clothing.
However, note this difference (which is annoying for learners):
This is a new pair of trousers.
These are new trousers.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.