I just started a jeet kune do classes a month ago, during the sparring parts I find it very hard to close the gap against people who have been doing this for much longer but I cannot understand (yet) how I can close the gap for going through their guard.
Practice at home footwork and angling. Speed is what will save you. When you move around a person they move faster because they just rotate on the pivot point. Timing your angled footwork lets you face their center point outside of there strikes if timed right. Control fighting distance. JKD secret is to make the other guy move first into range where you intercept his actions. This is where you need to learn how to read a person. Also get rid of your own tells by shadowing boxing in a mirror and record your sparring sessions.
There were three techniques which helped me a lot (and still do) when I started sparring in JKD:
progressive indirect attack
jamming their attack (e.g. striking their hand is it goes towards me, the essence of jeet kune do is to intercept, destroy or prevent an attack from an opponent).
attack by combination (for example a simple 1-2-3 or jab, cross, lead long hook) a couple of times followed by a straight blast (remember the JKD straight blast is the most effective entry or finish weapon once the opponent gives us an opening, its also the fastest way to punch)
Relating to footwork the fastest way to advance longer distances (e.g. when pursuing an opponent or recovering form a retreat is to use a slide and step or forward shuffle) to gain shorter distances is the half step/jump with the lead leg e.g. lunging jab.
In essence for all fighting speed and mobility is the key. Cover your self, move constantly both your body around the opponent and your tools (hand and head movement) and attack. The effectiveness of an compound attack is that it will show an opening which can be exploited by the attacker.
Stopping on a failed attack or stopping to think of what next is allowing time for the opponent to react, it also opens the possibility in your mind that the opponent is going to win.
One failed attack should be immediately be succeed by another attack on another angle, then another. Like water flowing to a wall flow around it till you find a hole you can pass trough.
And remember the entire human body is a target. There are no safe zone. We are no scoring points here. A hit on the arm can be effective and more achievable then a hit on the head since the arm is more exposed, especially if you can hit it with an elbow or leg. Hips, shoulders, joints, and lower body are all excellent areas.
But generally there is one principle to have in mind, to miss-quote Sifu Lee :
Be like water, flexible and adaptable yet strong and violent.
during the sparring parts I find it very hard to close the gap against people who have been doing this for much longer
Great! That suggests your school is teaching good technique such that more training will make you hard for people outside to hit. Don't be discouraged by that, but by all means take it as a challenge to make up the ground as quickly as you can, as well as an indication that careful observation and contemplation of what those more experienced people are doing really - combined with similar attention to the instructor and diligent practice - will help you get there too.
As for techniques - closing the gap is largely about recognising how your opponent might attack you, and sliding forwards in a way that cuts off all the opponent's direct lines of attack, leaving them to make slower round-about attacking movements that you'll have time to see and react to. A good way to start perceiving and relating to this "problem space" is to consciously study the lines from people's elbows through their fist to the place they might want to punch. If their fist isn't directly pointing at you with their elbow behind, they'll have to swing their forearm towards you in an arc instead of being able to drive it in a straight-line jab/cross, if they try to move from such a position into a straight-ish punch and you put your arms or hands anywhere inside that arc as you move forwards they won't be able to complete their motion and actually get their fist moving towards their intended target (e.g. your face). Once you're comfortably able to perceive and intercept the lines they must attack along, you can apply "intercepting fist" concepts to deflect them while punching/chopping/elbowing etc. in counterattack, as well as trap their limbs effectively. You can accelerate your learning of these concepts by reading some JKD books and other sources, but be careful not to cement bad habits before your instructor can set you on the right path. Some patience is required - just like nobody can age whiskey 20 years in a month.
A similar thing goes for kicks... see if you can be just "outside" the line they can comfortably front kick forwards to, such that they'll need to rock back a little while rotating towards you before delivering a kick - that way you're safer closing the gap, have some time to see their attack, and can either attack first or counter.
And given they're more experienced, watch how you get stuck... try to do what they do to you to them and see how they stop you, then try to stop them the same way. Experiment and don't be afraid of getting an extra knock or two along the way... it's the only way to really learn what works, build your reflexes and expand your comfort zone and competencies.
Finally, study your timing, and look to close just after they've decided to do something. Feint a little and if they tense up do it again and slide in behind it. Don't be afraid to throw a few techniques to keep them busy even if you don't seriously expect them to be terribly effective... experience will distill what works eventually, and having them easily block is better than them being 100% focused on hitting you.
It is hard to do, especially against a younger or more experienced adversary. I am 60 plus and not as fast as I used to be but in my dojo I tend to wait for my opponent’s move and then counter attack to break in. It’s hard, no doubt about it but timing is the key. When he goes, you block and go like hell. Sometimes it works, sometimes it doesn’t.