Do airlines still buy brand new 767s?

There are two different types of buyers to consider: commercial air carriers providing revenue passenger service, and air freight operators. Your question refers to not seeing “new” 767s on the ramp, so I’m assuming you’re referring to the former.

Airline orders placed with the big airframers are a major aspect of the competitive rhetoric among them. To my knowledge, Boeing hasn’t formally declared themselves out of the business of building passenger versions of the Boeing 767, but the word on the street about the 767–300 when it first entered service was that it was basically a gap-filler designed to support interim demand as production of the Boeing 787 Dreamliner was ramped up. All currently produced and delivered 763s appear to be freighters.

According to AirFleets (…) — which I’ve found really reliable over time — not a single passenger operator has taken delivery of a 767 manufactured within the past three years. That seems a pretty strong indicator that the customers have moved on to other types.

As far as the cargo operators are concerned, though, Boeing 767s remain extremely popular in their freighter incarnation. As the Motley Fool noted a couple of years ago, “Though the 767 entered service in 1982 as a passenger plane, it’s the aircraft’s freighter version that’s kept the program alive.” (The Orders Are Piling Up for Boeing’s 767 and 747 — The Motley Fool) While FedEx Express continues to buy new aircraft, a lot of the current demand from that sector is being met through conversions from passenger-configured 767s; for example, see Atlas Air orders nine Boeing 767 converted freighters; UPS orders converted cargo planes.

As long as we look at the question as airlines buying 767s they definitely do. Most cargo companies operate as airlines and 767 is still one of the most preferred wide body cargo aircraft in the market due to extended range of some models. Since long range cargo planes don’t have an increasing demand there is no stable number of orders for 767s though.

Passenger airlines don’t order 767 anymore but 767–300ER used to be the placeholder for the new 787 Dreamliner as a very efficient plane and had been built even in recent years.

The 767 is the first twinjet wide-body type to reach 1,000 aircraft delivered. As of May 2017, Boeing has received 1,204 orders for the 767 from 74 customers; 1,099 have been delivered.

No, they don’t. The 767 is in its golden years; its still being made by Boeing but only for cargo.