Simmonds, who is in the final season of a six-year contract he signed Aug. 16, 2012, can become an unrestricted free agent July 1. The 30-year-old forward has 27 points (16 goals, 11 assists) in 62 games this season.
Selected by the Los Angeles Kings in the second round (No. 61) in the 2007 NHL Draft, Simmonds has 471 points (242 goals, 229 assists) in 824 regular-season NHL games and 21 points (eight goals, 13 assists) in 42 Stanley Cup Playoff games.
"Wayne Simmonds brings not only offensive consistency that he's had through his career, I think he's had four 20-goal seasons, but he's a presence on the power play," Predators general manager David Poile said, "and he really has good hands around the net and he's been very effective at scoring and helping on the power play for the Philadelphia Flyers."
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Simmonds, who was acquired by the Flyers in a trade with the Kings on June 23, 2011, scored at least 24 goals in six seasons in Philadelphia, including an NHL career-high 32 in 2015-16. He played in his first NHL All-Star Game in 2017 and was named MVP.
"If we weren't prepared to sign [Simmonds] now, it was important to get some assets back," Flyers general manager Chuck Fletcher said. "Going into the summer, we have an awful lot of cap space. I was contemplating keeping Wayne for the rest of the year. But ultimately you have a chance to get a 24-year-old forward who can help your team now and for a few more years after that."
Hartman, who can become a restricted free agent July 1, has 20 points (10 goals, 10 assists) in 64 games this season. Selected by the Chicago Blackhawks in the first round (No. 30) in the 2013 NHL Draft, Hartman has 83 points (40 goals, 43 points) in 226 NHL games. He was traded to the Predators by the Blackhawks on Feb. 26, 2018.
Fletcher said he expects Hartman to be in the lineup when the Flyers play the Buffalo Sabres at Wells Fargo Center on Tuesday (7 p.m. ET; NBCSN, NBCSP, NHL.TV).
"We'll see how he fits," Fletcher said. "But he should be a guy that fits in our top-nine and should step into the role Wayne had and we'll see how (coach) Scott [Gordon] uses him."
NHL.com correspondent Robby Stanley contributed to this report