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To simplify the expression \((7x^2 + 13x - 19) - (4x + 7 - 16x^2)\), we first distribute the negative sign across the second set of parentheses:
\[
(7x^2 + 13x - 19) - 4x - 7 + 16x^2
\]
Combining like terms, we first combine the \(x^2\) terms:
1. \(7x^2 + 16x^2 = 23x^2\)
Next, we combine the \(x\) terms:
2. \(13x - 4x = 9x\)
Finally, we combine the constant terms:
3. \(-19 - 7 = -26\)
Putting it all together, we have:
\[
23x^2 + 9x - 26
\]
Thus, the expression \((7x^2 + 13x - 19) - (4x + 7 - 16x^2)\) simplifies to:
\[
\boxed{23x^2 + 9x - 26}
\]