Instead of this
<?php
$sector_applications = get_sub_field('sector_applications');
?>
Use this
while ( have_rows('sector_applications') ): the_row();
And then call your sub_fields. It's a an repeater inside an repeater. Like a foreach loop inside a foreach. You called it like it's an field but actualy has rows.
have_rows() – allows us to loop through the available rows in a repeater / flexible content field
get_sub_field() – returns the value of a sub field (from the current repeater in “has_sub_field”)
the_sub_field() – displays the value of a sub field (from the current repeater in “has_sub_field”)
More information and an good example you can find in ACF | Working with Nested Repeaters
I think the problem is here, I have modified your part of the code
<?php
while ( have_rows('application_sectors') ): the_row();
$image = get_sub_field('image');
$heading = get_sub_field('heading');
while ( have_rows('sector_applications') ): the_row();
?>
Your structue is this: Repeater
But you don't get into another repeater...
In my example you have
Repeater
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