Who do you recommend to drive me from ostuni to positano ?

If you use the Search function on this website, then choose "Travel Forum", you'll find quite a few mentions of Daytrip.com, because a number of posters here have used that company in various European countries. (I have not.) Here's a list of links from the last 2 years:

Forum search results for "daytrip.com"

Note that Daytrip.com is a third-party in this process. It connects travelers to transportation providers; it doesn't employ drivers itself. I don't remember seeing any complaints about the company.

js, what you're proposing will be very expensive. Just choosing a random date, Daytrip.com is coming up with a price of between $800 and $900: it's a long trip. Just don't want you to be surprised....

Editing to add: gas prices are currently taking a hit, thus may affect private transfer rates.

We will be using daytrip.com in May so no firsthand experience yet
But have you considered taking train at least part of the distance-perhaps to Caserta then use a driver
Would save several hundred dollars

I would not use a third-party company like DayTrip.....why add an extra level of pricing?

We've booked a driver from Naples to Matera, in May, with a possible lunch stop...the company is Aldo Limousines.
It's not quite as long as journey as the one you are looking for, about an hour shorter, but the price is nowhere remotely close to $800.

I've had great experiences using private drivers for occasional transfers and day trips in southern Italy. A few times my hotel recommended a driver so you might inquire and compare pricing.

We have used Aldo drivers, also, and I would highly recommend them. Safe travels!

https://www.aldolimos.com/

You can get a quote if you give them your details.

Considering it is ~240 miles one way and takes 4.5-5 hrs, an estimated cost of $800 doesn't look too far off. The driver will be driving at least 9 hours and almost 500 miles.

Thank you all for your input.
In the end, we went with “positano drivers” whom we had used before and know are reputable and reliable. Their price was also lower than the others.

Care to share how many in your party and the cost?