How can I get boarding card in UK Gatwick airport with Direct Airside Transit Visa (DATV)?

There are two options available to you.

One option is to take advantage of the fact that BA offer Online Checkin and Mobile Checkin. This opens up 24 hours in advance. You head to the BA website or mobile app, type in your flight details (or BA Executive Club details, if you're a member and have associated it with your booking). You can then enter any advanced passenger information that's needed, pick your seat, and complete checkin. If checking in online, you're then given your boarding pass to print. With the mobile app, it downloads the boarding pass to your phone/tablet, and shows it on that. This option lets you sort it all out a day in advance, and as a bonus lets you pick a good seat!

Otherwise, when you land at Gatwick Airport, you'll need to follow the signs for Flight Connections. There's a lot of information on it on the airport's website, including an example of the bright pink signs you need to follow. That'll take you to an area where all the airlines have counters. Find the BA one there, queue up, show your passport, and they'll issue you your boarding pass. You can then clear security, and go to wait for your flight.

Speaking of flight connections, I presume from your question that you're flying Iran -> Istanbul, Istanbul -> Gatwick, Gatwick -> elsewhere. As such, you'll be going through flight connections at Istanbul when you arrive in Turkey. BA fly to Istanbul, so if the timing is right, you might even be able to get a BA agent in Istanbul to print your boarding pass there. If not, it's fine (and quite normal) to get it when you reach Gatwick.

(Because Turkish Airlines is in Star Alliance, and British Airways is OneWorld, it won't be possible for Turkish Airlines to issue you with a BA boarding pass when you check in).