Possession, just as always, with flexible senses - here, in an abstract sense by the time known as "now".
"The Paul, who is in the possession (的) of now (现在) - Now's Paul - already (已经) has realized (了) the age of 63 years (岁)."
Or in a more succinct form, still preserving the cognition,
The Paul of now already attained 63 years of age.
Or, in a more colloquial, conventional form,
As of now, Paul is already 63.
By the "already" (已经), it sounds like there was some expectation elsewhere in the text that he was not so old by now.
ADD, see comments: This whole unit 现在的, in this instance, can also be understood as an adjective phrase - in that sense, it signifies that "nowness" is a quality held by Paul (effectively, the inverse of the interpretation described above), so the "Paul of the present time", or the "Paul with existing-in-the-present-time-ness". X的 in general is an adjective meaning "Xness-possessing". This is actually the most common interpretation, it's just that here, with this specific term, we have an alternative one that also makes sense as well, but in other cases one or the other will be clearly more sensible.