To answer your explicit question: One does it using the Project tool. ArcToolbox > Data management Tools > Projections and Transformations > Feature > Project
To trouble shoot your issue, it might help to more precisely define "not lining up". Have you tried going the other way (UTM to geographic)? That might throw some light on matters. Some times an incorrect UTM zone has been specified somewhere, which can look confusing if one does not know what that looks like...
The best advice i can give you is check on what kind of coordinate system you are importing the points/shapefile to, i have ran into this problem many times. With the picture i have provided gives a better idea of how with even the right kind of coordinate system clipping can not solve. When you say that they are "not lining up" how far would they exactly be? a state away? or a city away? if they are very close to each other the clipping tool might be of some help. Hope this might have helped you out some into answering your question.
Thank you the above replies. I just found out the original shapefile is incorrected created. Therefore, the shift (not lining up) with the target shapefile is not solvable by convertting coordinates system.
My new questions is, how to line up the UTM 54N shapefile with a 500m grid map generated based on latitude and longitude?