That looks like a 2" eyepiece adapter as used on Celestron telescopes, among others.
My 2nd-hand Celestron NexStar SLT 130 would originally have had both a 1 1/2" and 2" version of the adapter, depending on which eyepieces you want to use, but I only got the 1 1/2" adapter - I guess the original owner lost the 2' adapter because they couldn't work out what to do with it either! If you only have one size of eyepieces and accessories, you never need the other adapter, so it would be very easy to lose over time.
The adapter fits straight into the rack-and-pinion focuser and is held by two large thumb-screws in the focuser, and then the eyepieces fit straight into the adapter and are secured using the two smaller thumbscrews of the adapter.
When you say you can't focus your 1 1/2" eyepieces using this adapter - do they fit securely into the adapter, or do you need to use a 2" to 1 1/2" adapter tube? If you have to use an extension tube to get the 1 1/2" eyepieces to fit, it may be positioning them too far away to be able to rack in to achieve focus.
The attached photo shows my 1 1/2" adapter in my NexStar SLT 130 with a digital camera installed - you can see that the eyepiece / camera has to be very close to the top of the adapter to be able to reach focus.
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