Replacing footage to a video with different frame rate - how to make timeline clips not slip?
Not sure I get what you're describing, but here are some ideas:


Right click on your clip in the timeline and select the "Speed/Duration" option. Have fun.
If you want that added clip to have its own frame rate within your sequence, perhaps you should start seeing it as an effect. So treat it as such: once your edit is done (picture lock), import it in After Effects, treat the portion of it that you need as you see fit. Export it thus transformed. Import that new clip in your timeline, place it over its old version and never worry again about a change of frame-rate.