* China's Juneyao Airlines took delivery of new 787 on Thursday

* China suspended most Boeing orders, deliveries in 2019

* 787 deliveries could herald lifting of 737 MAX freeze

Dec 22 (Reuters) - Boeing's first direct delivery of a 787 Dreamliner to China since 2019 landed in Shanghai on Friday, a step that could hasten the end of China's freeze on deliveries of the firm's profitable 737 MAX after more than four years.

Privately owned Chinese carrier Juneyao Airlines on Thursday took delivery of the 787-9 aircraft, which Boeing said then departed for China from Everett Paine Field in Washington state.

The flight landed in Shanghai around 4:20 p.m. local time (0820 GMT), the airline said.

China suspended most orders and deliveries of Boeing planes in 2019 after the 737 MAX was grounded worldwide following two fatal crashes.

A restart of MAX deliveries would represent a reset of Boeing's relationship with China and create an opportunity for the company to offload dozens of planes in its inventory, and pave the way for a larger breakthrough in deliveries and orders.

The company expects China to account for 20% of the world's aircraft demands through to 2042.

Boeing last delivered a leased Dreamliner plane to a Chinese customer in 2021, but no 787s have been handed over directly to Chinese airlines since November 2019.

Analysts had forecast the resumption of Dreamliner deliveries to China after consultancy AAP/AIR this month reported preparatory flight activities for a 787 designated for Juneyao Airlines, registered as B-20EQ.

Twelve of the 60 undelivered 787s in Boeing's inventory are dedicated for Chinese operators, analysts Jefferies said.

Boeing's business with Chinese airlines could be affected by the political ties between Washington and Beijing, which have recently improved.

Last month, U.S. President Joe Biden and Chinese President Xi Jinping held their first face-to-face talks in a year, and on Thursday the top U.S. military officer spoke to his Chinese counterpart in the first such conversation in over a year.

MAX PROGRESS

On Wednesday, trade publication The Air Current said Boeing had this month won a key clearance from regulator the Civil Aviation Administration of China (CAAC) allowing the planemaker to prepare MAX aircraft for delivery.

The safety bans have been lifted as existing MAX planes are flying inside China, but new deliveries have remained on hold.

The CAAC's deputy head on Dec. 8 told a Boeing executive in Beijing the planemaker was welcome to deepen its development in the Chinese market, Reuters reported. The Air Current, citing unidentified sources, said the regulator's clearance was granted that day.

Individual MAX deliveries to China still need approval from China's National Development and Reform Commission (NDRC), the Air Current report said.

Boeing told Reuters it is ready to deliver to customers "when that time comes".

The CAAC and NDRC did not respond to requests for comment.

A 737 MAX designated for China Southern Airlines flew from Boeing Field in Seattle to Boeing's nearby facility in Moses Lake, Washington, and back on Wednesday afternoon, according to data from flight tracking website FlightRadar24.

Analysts from Jefferies and Deutsche Bank said in investor notes that it appeared to be a customer acceptance flight - a test flight operated by an airline pilot that occurs before delivery.

MAX deliveries to China could provide some upside to Boeing's $10 billion free cash flow target for 2025-2026, as that projection did not factor in potential deliveries to China, analysts say. (Reporting by Sophie Yu and Lisa Barrington; editing by Miral Fahmy)