There are a bunch of older EDGE guys left out there who aren't going to be on the field every down. I'm sure the Rams will add one or more of them. They will probably add one that has been released, or wait until the initial FA period is over to avoid giving up any of the compensatory picks they are accumulating.
EDIT. Here's PFF's best remaining, some aren't great 3-4 fits.
Edge Jadeveon Clowney
Clowney is one of the better run defenders in the league and he has the speed and power to move around the defensive line to create mismatches in pass-rushing situations. He's a No.2 pass-rusher and should not be relied upon as a No. 1 option.
Edge Melvin Ingram III
Ingram is still an effective all-around player, but he's likely best as part of a rotation at this point in his career. He can play the run on the edge or rush from any alignment.
Edge Justin Houston
Houston fits into the cluster of edge defenders in this free-agent class who can still provide value to a defense but are best utilized situationally at this stage of their career. He has shown in his time with Kansas City, Indianapolis and Baltimore that he can operate both as a 4-3 defensive end and 3-4 outside linebacker.
Edge Jerry Hughes
Hughes has graded out in the 90th percentile or higher of edge defenders in pass-rush grade and pass-rush win rate over the past three seasons. Turning 34 years old in August means that ability is best used situationally at this point, but Hughes makes sense on a defense in need of another pass-rushing specialist off the edge.
Edge Derek Barnett
Barnett does not stand out in any one area, but he can play the run and he's a mid-tier pass-rusher. Ideally, he'd be part of a 3-man rotation on the edge, but he can provide a quality 600-800 snaps as a starter.
Edge Jason Pierre-Paul
The last two edge defenders in their 13th season or higher to play a single defensive snap were Terrell Suggs and Lorenzo Alexander in 2019. The days of Pierre-Paul logging over 1,000 snaps like he did in 2020 should be over, but he can still contribute as part of a rotation that keeps him fresh.
Edge Arden Key
Key has never been a great run defender, but his breakout 2021 season showed that he has a role rushing the passer from multiple alignments.
Edge Dante Fowler Jr.
Fowler isn't exceptional at any one thing, making him a rotational player at this point in his career. He can create some pass-rush, but it's rarely explosive or effective, and he's a reasonable run defender if he can cut down on the missed tackles.