To solve the expression \( \frac{4}{15} - \left(2 \frac{9}{15} - \frac{11}{15}\right) \), let's break it down step by step.

First, simplify inside the parentheses:

1. Convert the mixed number \( 2 \frac{9}{15} \) to an improper fraction:
\[
2 \frac{9}{15} = 2 + \frac{9}{15} = \frac{30}{15} + \frac{9}{15} = \frac{39}{15}
\]

2. Subtract the fractions inside the parentheses:
\[
\frac{39}{15} - \frac{11}{15} = \frac{39 - 11}{15} = \frac{28}{15}
\]

Now, the expression becomes:
\[
\frac{4}{15} - \frac{28}{15}
\]

Since the denominators are the same, subtract the numerators:
\[
\frac{4 - 28}{15} = \frac{-24}{15}
\]

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
\[
\frac{-24 \div 3}{15 \div 3} = \frac{-8}{5}
\]

So, the simplified result of the expression is:
\[
\frac{-8}{5}
\]

Or, as a mixed number:
\[
-1 \frac{3}{5}
\]