Using MIDI routing, you can send the notes to a different instrument in Renoise. And, using audio routing, this instrument can be playing in any track you want. Note that the receiving instrument will not be able to trigger a phrase itself when triggered via MIDI routing.
Capturing/recording the notes as they are played requires a different approach. Unfortunately, this is a bit more tricky - you'd need to assign the instrument you want to capture to an external MIDI output, and then use something like a virtual MIDI cable to route the notes back into Renoise. You can pick a specific instrument/track as the receiver by heading into the MIDI Input options.
With virtual MIDI cable, you might have to tweak the latency to find a good setting. Also, pick the best drivers - WDM-based MIDI on Windows, for example... I think there's a lot more information floating around about virtual MIDI cables on these forums, I tend to use loopMIDI myself.