Upper bound

#include <iostream>
#include <vector>
#include <algorithm>

int main() {
    std::vector<int> v = {5, 6, 7, 8, 9, 15, 17};
    int x = 9;
    auto it = std::upper_bound(v.begin(), v.end(), x);
    int cnt = v.end() - it;
    std::cout << "Number of elements greater than " << x << " is " << cnt << std::endl;
    return 0;
}

if the array is sorted you can use binary search to get the result in $$$O(log n)$$$ time, also C++ has a prebuilt function named upper_bound which does the same thing, if the array isn't sorted you can sort it first in $$$O(n log n)$$$ time and then use binary search or, iterate over the array and calculate it with a for/while loop in $$$O(n)$$$

You can do binary search or use built-in functions in C++ like upper_bound (strictly bigger) or lower_bound (equal or bigger).