PHILADELPHIA — It wouldn’t be until nearly a month after the July 31 non-waiver trade deadline last summer that the Mets made an overlooked move that left a lasting impact.

That’s when the Mets sent a pair of minor-league arms to the Diamondbacks for Addison Reed, a one-time closer whose struggles had prompted a demotion to the minors earlier in the season.

Nearly a year later, Reed has emerged as one of the top relievers in baseball, a steady and versatile weapon deployed mainly in the eighth inning as a setup man for Jeurys Familia.

“He’s saved us in the back end of the bullpen,” manager Terry Collins said Saturday.

The Mets again are in the market for a reliever and hope to find another hidden gem. Perhaps a move will come before the Aug. 1 non-waiver trade deadline, perhaps it will come after. But sources say they are targeting an experienced righthander to fill out a bullpen that continues to be a strength.

Mets relievers have a 3.20 ERA, third best in the National League and sixth best in baseball.

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Lately, they’ve been even better. In the last 12 games, the Mets’ bullpen has a 1.64 ERA with 48 strikeouts.

Heading into Saturday’s action, Reed’s 2.09 ERA ranked seventh among all relievers with at least 40 innings. It’s an improvement that pitching coach Dan Warthen attributes to a tighter slider and adjusted fastball.

But Collins echoed sentiment shared by the front office that the Mets could use another arm to guard against overuse. “If we continue to have close games, there’s going to be nights where we’ll have to turn to somebody else,” he said.

Jim Henderson slotted into that role, pitching to a 1.08 ERA in April, but he faded and landed on the disabled list June 21 with right biceps tendinitis.

The Mets signed Antonio Bastardo to a two-year, $12-million deal in the offseason. They envisioned him as another experienced reliever to work in high-leverage situations. But he has flopped, posting a 4.91 ERA. His role has been marginalized since a brutal spring training that spilled over into the season.

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Hansel Robles, 25, has a 2.93 ERA in 38 appearances. While he has pitched well, the Mets place value on experience.

They nearly signed Kevin Jepsen after his release from the Twins with a 6.16 ERA. The righthander ended up reuniting with the Rays.

And skepticism exists within the organization about the cost benefits of a higher-end reliever such as the Brewers’ Jeremy Jeffress.

It’s possible the Mets’ biggest move will come later in the process. For instance, their big bullpen move last summer involved trading for Tyler Clippard, and the Mets figured Reed would be non-tendered because of the $5 million he was expected to earn in arbitration. By season’s end, the thinking had changed. Clippard left as a free agent and the Mets retained control of Reed, signing him to a $5.3-million deal that has proved to be a good investment.