I plan to start my Ph.D. quite late at age 31. I wanted to know if this would have any implications on my career if I decide to stay in academia and apply to faculty positions after completing my Ph.D.
Officially, age discrimination is illegal in hiring in the USA after the age of 40, but it still happens. Still, you won't find hard cutoffs in grant language or tenure tracks that have to do with your date of birth, but many impose timelines that initialize the year you finish your PhD, or the date you got hired, etc. 1 Another thing to consider is how comfortable you want your life to be, and how many years people spend in your PhD program and in postdocs. The pay in grad school is very low, so it's hard to get any meaningful savings or a sizeable retirement fund. Postdocs in the US pay decently in some fields, but depending on your lifestyle it can still be tough. Postdocs with families in my field, for example, do seem to be squeezed.
Another factor is geography. Jobs in academia can be competitive, and you don't have a lot of control over where you live (again, depending on the field). So think about how late in life you want to be settled in one place. If you have a partner or anticipate having one, you may have to separate for long periods of time if the geography of your jobs is incompatible. There are many long distance marriages in my field.
These problems are difficult for everyone, but they are a little easier to deal with early in life. You still have time to save up for retirement after you get a tenure track job, you have cushioning if your PhD takes an extra year or two, you're less likely to have children and other high expenses, and you may find starting over in a new place exciting rather than exhausting. These are just generalizations, and there are plenty of counterexamples, but they are factors to consider in your own life before going down this road 10 years later than most people get started. If you get unlucky you could be looking at being well into your 40s before you have a stable job in a place you plan to settle.
But this all really depends on your field and your program.