There will most likely be a visual indicator. Note that the correct period is 7 days instead of 4 days:
"BW: Grimwulf asks “How does one actually die of old-age, do I just fall over dead in the middle of the street when the timer expires?”
Caspian: [...] We mentioned that vitality bar earlier, the way this is going to work is, you will be playing and hopefully you’ll notice your character starting to get older, their animations are changing a little bit, it should be obvious they’re advancing in years.
But if say, you have been misbehaving a lot, such that you’ve shaved off years of your life, even in your early 30s or 40s, you’re approaching the end of your life, you will notice that that vitality bar, upon waking up the next day has a slight sliver of black in it, and that black sliver will advance over the next 4 [Editor: Correct number is 7; correction mentioned later in the Q&A] days, until it accumulates and consumes your whole vitality bar. When that black shadow that is hanging over your vitality bar reaches 100%, your character is dead.
BW: Follow-up to that, “will I know how time I have left when I am close to dying of old-age?”
Caspian: Yes, when you see the black bar you have 4 [Editor: Correct number is 7; correction mentioned later in the Q&A] days."
from an old Q&A session
Here is a short explaination on what the vitality bar is supposed to be in this context:
"Caspian: [...] The secondary stats are things that are specific to combat, there are those as well as things as vitality and energy which are the thing you rely on when you move about in the world. Very quickly from the moment your character wakes up , they have a full vitality bar and as they go about the day doing things, like running, walking, sprinting, being in combat, forging or using their other skills the vitality bar will gradually go down.
The hungrier they are, the thirstier they are, the fast the vitality bar will go down. So this creates a meta will players kinda have to stop periodically, eat, take breaks and occasionally even rest in order to get their vitality bar back to full. Things that are high impact like sprinting, engaging in combat will actually drop the vitality bar as well and that’s much faster.
And the amount of energy you have is tied to the current vitality so if you’ve been out adventuring all day and you engage in combat with somebody halfway through your journey, you’re going to be in serious disadvantage because you’re tired and fatigued, where as if it’s a fresh start and you have lots of vitality you ultimately have a better chance doing those high impact things like fighting."
from an old Q&A session