Yes you can do that in Design Rules - Default - Clearance. In Clearance you will see Drill and you can use that to set clearance to Traces, Via, etc..
"trace to hole" = "drill to trace"
You say potayto, I say potahto...
Why won't that catch it?
Ahh - that did catch it. Thanx JD
But... here's the catch. Now I get a gazillion errors. The fab house can live with 4 or 5 mils clear trace to pad. They want/need 8 mils clear trace to hole - i.e. inner layer via hole with no pad. No way to set that near as I can see.
Set drill to trace, not pad to trace.
Here is what the rules look like in ASC export:
Fab shops usually spec that dimension to the "finished hole", so if you have a "drill oversize" setting you might change it to zero to get rid of some of the clearance errors... or just subtract 1/2 your setting from their "hole to" requirement to get the "drill to" number.