Watch the Level 3: Beginner Classical online guitar lesson by Andrew Leonard from Take 5: Beginner Classical
"Kemp's Jig" has four sections. In the Renaissance, these were called strains. The first strain could be thought of as the "A section". The second strain is a repeat of the A section with some added notes or "embellishments". We can think of these as written out improvisations.
The third strain would be equivalent to the "B section", and strain 4 is its repeat with embellishments. This is a common Renaissance practice. To extend the piece, you could repeat strains 1 & 3 by adding further embellishments each time. Once you have learned the piece, you might want to experiment with adding some of your own embellishments.
When performing this piece, remember you're playing a jig, so keep a steady beat. Even if you're learning this by practicing slowly, focus on your rhythm.
Also, this piece and "Greensleeves" make a nice pair. Both are from the same country (England) and the same period of time. The contrasts of mood and rhythm make them interesting to listen to back to back.
One thing to look be aware of: Measure 2 at 2:00 has a C chord shape. Don't confuse this with a C chord in first position. As I mention, you are playing a C# note. The chord is A major. Since the C# is the bass note, it's a first inversion. If you're unfamiliar with chord inversions, no worries, you don't need to know them to play the piece. This is a beginner classical guitar course, not a music theory class!
Oops! at 3:43 & 8:04 I say C instead of C#. The left hand finger is on the correct fret and the notation & tab are correct.