I sent a link to a random pintrest that has the brackets.

Its important that your existing posts are stable and free of rust ( as the OP's posts are) and a relatively heavy wall pipe. Sometimes you can add an interior sleeve to add rigidity if it's light wall. Typically you'd have 2 horizontal stringers for 3/4/5' tall fence meaning you'd need two of these brackets per post. 6/7' need 3 horizontals, thus 3 brackets per post.

If your posts aren't tall enough sometimes you can add an exterior sleeve to extend them. Chainlink pipe comes in funky sizes, to measure take a tape across the top of the post and go to the 1/8"

1 3/8 is common for dog kennels and residential toprail. 1 5/8 is a common line post size for residential line posts and commercial toprail. 1 7/8 is a common size for residential terminal (corners and ends) posts or light commercial line posts

2 3/8 and 2 7/8 are typically commercial applications.

Typically the smaller pipe sizes nest well, depending on wall thickness so you can figure out what length and diameter sleeve you need based on what you currently have.

It was also mentioned above to watch post spacing, I would agree that's its not ideal to go over 8' centers, you can get a post on a base plate to set as an intermediate if you are going on concrete / on a wall as the OP is. For a standard DIY project install I'd just dig and set a post in between the existing. Granted this is not how I would do it in my business but it works for a homeowner project to cut the labor.

I hope that helps, hit me with any other questions.