* Q3 operating profit $286 mln vs $272 mln estimated

* Firm says expects Q4 order pickup from a key customer

* LG Display is an Apple supplier

* LG says expects Q4 profit to "improve significantly" (Updates with comments from LG Display, background on Apple)

By Se Young Lee

SEOUL, Oct 26 (Reuters) - South Korea's LG Display Co Ltd on Wednesday said it expects strong fourth-quarter earnings as the Apple Inc supplier tipped growth in shipments of medium-to-small sized panels to a key client it would not name.

Apple on Tuesday warned of supply constraints for its new iPhones, particularly the larger-sized iPhone 7 Plus, suggesting it may not be able to fully capitalise on rival Samsung Electronics Co Ltd's decision to scrap the fire-prone Galaxy Note 7 smartphone.

LG Display, which analysts say counts on Apple as its top client by revenue, did not say what devices the unnamed customer was buying the screens for.

It expected the overall revenue contribution from medium-to-small size panels - used for products such as smartphones - to rise in October-December from the third quarter.

"The upwards trend of panel prices is expected to continue in the fourth quarter due to the growing trends towards large-size panels," LG Display Chief Financial Officer Don Kim said in a statement.

"In addition, profits in the fourth quarter are anticipated to further improve significantly."

The world's top liquid crystal display maker said July-September operating profit fell 3 percent to 323 billion won ($286.12 million), versus a Thomson Reuters StarMine SmartEstimate of 307 billion won derived from a survey of 11 analysts.

LG narrowly avoided losses in the first two quarters of the year as sluggish global growth undercut demand for consumer electronics, but analysts say panel prices have been rebounding in the second half as smartphone and television makers place new orders to gear up for the year-end holiday shopping season.

While revenue contribution from devices such as smartphones would increase in the fourth quarter as clients launched new products, LG said its total shipments volume by surface area would be about that of July-September as total production capacity would remain similar.

The South Korean firm said third-quarter display shipments in surface area terms rose 9 percent from the previous quarter, while average selling prices climbed 10 percent.

Data from researcher IHS shows that panel prices for products such as smartphones, televisions and monitors have been trending higher in recent months, with average prices in certain categories rising more than 10 percent in October from the previous month.

Revenue for the period fell 6.1 percent to 6.7 trillion won, compared with a Thomson Reuters StarMine SmartEstimate of 6.4 trillion won. ($1 = 1,128.9000 won) (Reporting by Se Young Lee; Editing by Stephen Coates)