I was going to do my Grade 3 piano, until the pieces I had learned had gone past the deadline for when I was going to take my examination. Therefore, I had got frustrated, so my Piano teacher asked me if i would like to skip a grade? My parents said yes, but I am concerned if there are any long-term consequences? Consequences include anything like my future e.g. university or QCF Points..
The only grade that you can't skip is the theory exam (Grade 5 theory, or an equivalent - see http://us.abrsm.org/en/our-exams/information-and-regulations/prerequisite-for-grades-6-8/) which is a prerequisite for practical grades 6-8.
It's "normal" for good students to skip one or two practical and/or theory grades below grade 5, unless they are examination junkies who want to take two sets of exams each year, and live in a place where it is possible to do that.
Should be no problem whatsoever to skip a grade or two. If your piano teacher thinks you are ready for Grade 4, then go for it! (It was rather a long time ago, but I only ever did 2, 4, 5, 6, 7, 8, and arguably 8 is the only one that matters; the others just help you pace yourself.)
The grades are cumulative, not task-orientated. That is to say, if you skip out Grade 3, you won't have missed anything that's ONLY in Grade 3. It's not like skipping a chapter in a textbook. So, if you're good enough to move straight to Grade 4, no problem.
I took my Grade 6 and grade 8 exams with the Canadian RCM, which is very similar to the ABRSM. I wanted to skip grade 7 entirely, but my teacher strongly advised me to continue with grade 7 and simply not take the exam. This was very much the right call — the difficultly level between 6 and 8 was significant, and I was not capable of playing many of the Grade 8 pieces until I had another ~500 hours of practice and ~50 hours of instruction under my belt with the grade 7 material.
Since you are earlier on, the difficulty gap might not be as extreme. However, I would still recommend that you stick with whatever grade material matches your ability (as assessed honestly by yourself and your teacher). If learning the grade 3 material has taken you extra time, then I would definitely recommend that you continue investing the time needed to master it before moving on. If it's simply that you missed the examination date and are ready to start grade 4, then do so; the other answers have indicated that you will not be penalized in any way by the ABRSM.