New crown with existing removable clasp partial denture. Just got permanent crown on tooth #18 for the first time on this tooth.

If the crown is tilted, and you're not happy, I would make sure that I bring that to the dentist's attention.  She will likely redo that crown at no additional cost.  If there is metal that is digging into your gums, bring this to the attention of the dentist,  I hope this helps.  

One of the more challenging procedures we do as dentists is to make a new crown and fit it under an existing partial denture. Having said that, I'm sure your dentist can adjust the clasp holding the partial in, as well as adjust the underside of the partial so it doesn't rub too hard on your gum in that area. You should not need to remake the crown. This is a very typical situation.

You really need to return to the dentist and let him handle this problem. The clasp might be the wrong shape. The new crown might be the wrong shape. Difficult to tell exactly what the problem is without seeing it directly. Very difficult to make a crown fit within an existing denture.