Clayton Kershaw might not be the Dodgers’ opening-day starter next year.

If Kershaw must undergo surgery to repair his ailing right hip, he isn’t expected to be pitching in the major leagues until the middle of May, according to people familiar with his condition who were not authorized to speak publicly about it.

Kershaw’s decision on whether to have an operation will be made after Kershaw receives a second opinion from Dr. Bryan Kelly on Tuesday in New York. Kershaw was unable to make his scheduled start for the Dodgers on Sunday.

Kershaw, 24, has been the Dodgers’ starter in each of their last two season openers.

Kershaw is under contract next season for $11 million and won’t be eligible for free agency until after the 2014 season.

The Dodgers have five other starting pitchers under contract for next season: Josh Beckett ($15.75 million), Ted Lilly ($13.5 million), Chad Billingsley ($11 million), Aaron Harang ($7 million) and Chris Capuano ($6 million).

Billingsley suffered a season-ending elbow injury and could have surgery this off-season. Lilly is scheduled to undergo a shoulder operation Friday.

Lilly is expected to be ready for spring training.

Elbert done for season

Left-hander Scott Elbert is scheduled to undergo a season-ending operation Wednesday to clean up his throwing elbow.

The surgery will be performed by team physician Dr. Neal ElAttrache. Elbert is expected to be ready for the start of spring training.

Elbert last pitched Aug. 26. The next day, he was put on the disabled list for the second time this season.

Elbert pitched a simulated game Friday.

“The next day, he went out to play catch and it was back, same thing,” Manager Don Mattingly said. “So we knew he was done.”

Elbert, the lone left-hander in the Dodgers’ bullpen for most of the season, posted a 2.20 earned-run average in 43 appearances.

“He felt bad,” Mattingly said. “He tried everything. He had two shots. He tried to wait it out. Every time he extended himself, it came back.”

With Elbert unavailable, the Dodgers have only two left-handers in the bullpen: veteran Randy Choate and rookie Paco Rodriguez.

Choate, who was acquired from the Miami Marlins in July, has a 3.09 ERA in 29 appearances for the Dodgers. Rodriguez, who was drafted from the University of Florida this year, has pitched in four games.

A record day

If anything, the Dodgers made history in their 5-2, 12-inning defeat to the St. Louis Cardinals on Sunday.

The Dodgers used 10 pitchers, the most they have ever used in a single game in the history of the franchise.

Starter Stephen Fife pitched five innings and was followed by Shawn Tolleson, Choate, Jamey Wright, Rodriguez, Brandon League, Ronald Belisario, Matt Guerrier, John Ely and John Wall. Ely was charged with the loss.

Watching the parade of relievers made Kenley Jansen feel almost guilty. Because of medication he took to treat a heart condition, he won’t be able to pitch until Tuesday.

“Your arm is not hurting,” Jansen said. “You just can’t be out there. That’s the toughest part. These guys keep playing hard. It’s frustrating, but you can’t help them.”

dylan.hernandez@latimes.com