The correct word to fill in the blank is mastery.

Reasoning:

The sentence sets up a clear progression of skill. The phrase "Having established his competence" indicates that the author already proved he had a solid, adequate level of skill with his first play. The phrase "went on to show greater" signals that his second play demonstrated an even higher level of proficiency or expertise.

Mastery perfectly fits this context, as it represents a comprehensive, advanced level of skill that naturally builds upon and exceeds mere "competence."
Characterization is too specific of a literary device and does not directly parallel the general measure of skill implied by "competence."
Understanding and perception refer more to cognitive awareness rather than the demonstrated craft or skill of playwriting.
Insufficiency directly contradicts the positive progression established in the sentence.


Therefore, "mastery" is the most logical and precise choice to complete the sentence.