The Yankees added a veteran lefty to their beat-up bullpen on Thursday, though he did not receive the warmest of welcomes.

The club signed sidearm reliever Tim Hill to a major league contract and immediately threw him into the mix in an ugly 17-5 loss to the Orioles.

Hill pitched an inning and gave up a three-run home run on which all of the runs were unearned because of an error behind him.

Hill, 34, was designated for assignment by the White Sox last week and then released Tuesday.

He had posted a 5.87 ERA with 13 strikeouts in 23 innings this season.

But Aaron Boone said before Thursday’s game that the Yankees believed Hill was better than his surface numbers would suggest.

“Hopefully getting here, getting in our environment, he can become an important part of this,” Boone said. “We think he gives us a different look down there that can be valuable.”

Clayton Andrews was designated for assignment to make room on the 40-man roster.

Across parts of seven seasons in the majors — also spending time with the Royals and Padres — Hill has a career 4.30 ERA in 347 appearances, known as a pitcher that can generate a high rate of ground balls.

Boone said Hill had been on their board “for a few weeks” and that in a few of his rough outings with the White Sox he had just been “dinked and dunked to death.”

There was some of that Thursday, as Gunnar Henderson led off the inning with a chopper down the open third-base line for a double.

Then, after a pair of fielder’s choices — the second including a throwing error by Oswaldo Cabrera — Hill got tagged for a three-run shot off the bat of Anthony Santander.

The Yankees were in need of a fresh arm after the bullpen was forced to cover six innings in Wednesday’s 10-inning, 7-6 loss to the Orioles, plus Ian Hamilton landing on the IL.

But after using six relievers Thursday — plus Jose Trevino for the ninth — Boone acknowledged there are likely more roster moves to come before opening a series on Friday against the Braves.

A day after making his season debut, Gerrit Cole was feeling like he hoped to physically on Thursday.

”When I first saw him a couple hours ago, he feels good about things and where he’s at,” Boone said. “I think we’re in a good spot there.”

Nick Burdi is set to throw a bullpen session on Friday, his first since landing on the IL on May 24 with right hip inflammation.

The reliever did not throw for two weeks after his last outing on May 23, wanting to give the inflammation more time to subside after it previously sent him to the IL in April.

“Maybe I just might have overdone myself wanting to get back out there a little too quick,” Burdi said. “It kind of came back, was feeling it again. I do think this time down has been a little bit longer, but it’s feeling better. My plan is to hopefully be in games within the next few weeks and go from there.”

Scott Effross, who began a rehab assignment on Wednesday night by throwing a scoreless inning for Single-A Tampa, is expected to pitch again on Sunday.

Because of his lengthy layoff — he underwent Tommy John surgery in the fall of 2022 and then back surgery in December — Effross is expected to need most of the 30-day rehab clock to finish off his buildup.

“He’s got to get some games under his belt, no doubt about it,” Boone said. “So we’ll see how long that takes.”