Competition with your advisor? My PhD research interest is very aligned with my advisor. However, my concern is that if I want to stay in the academia, will my advisor become my competitor in the future?
You might end up as competitors someday.  I've never felt like I was in competition with any of my former students or my own advisor, but some people are hyper-competitive, and others are unlucky enough to end up in awkward situations, so your mileage may vary.

Even though it could happen, you shouldn't waste time in graduate school worrying about hypothetical future competition.  There are more important things to think about, and you shouldn't let these worries interfere with learning as much as you can from your advisor.

Ultimately, becoming a successful researcher means developing your own research agenda.  Over time, you should drift away from your advisor as you explore your own interests.  (If you don't, it's a bad sign.)  In particular, as you become an established researcher your advisor will no longer play a central role in shaping your scholarly interests, and competition with your advisor will not be much more likely or worrisome than competition with other senior people in your field.