Right now, I am running a 52-39 Crank and a 11-23 cassette. Lately I've been having some trouble on some big hills in the area and I was considering dropping down to maybe a 11-25 or 12-25 cassette. My question is if I need to get a whole new cassette, or if I could simply by new sprockets and and replace them on my current cassette (shimano ultegra 6600). Also, would I need to add links to my chain to compensate for the lager sprocket? (I'm using a short cage derailleur too). I tried using the search function, but I sort of got conflicting answers. I was wondering what everyone here though. Thanks guys

Before you start changing your sprockets, I recommend that you do a little homework regarding gear ratios:

https://sheldonbrown.com/gears/

I'd get a new cassette. Not all cassettes have the same number of ganged sprockets. You might also end up with a big jump otherwise.

on the chain, I'd install the cassette and then check it in Big-Big combination to see if the chain is too short before buying a new chain.

(depending on how worn your chain is you might need a new one anyway when getting a new cassette, but I haven't had this problem often, and I change cassettes from time to time to meet race requirements)

example:

my TT bike with 54/42 front normally has an 11-23 cassette. Sometimes I put a 12-27 on it for hilly TTs.

same chain.

but that chain is not very worn or stretched.

yeah, my chain def has a little less than 1k miles on it

well, depending on conditions that could mean anything. normally I can get about 5k (or more) out of a chain on a road bike. cyclocross will trash a chain (for me) in less than a thou.

It may be cheaper to buy a complete cassette than to buy a cog or cog-set. Cassettes are built of a combinations of cogs and cog-sets with several cogs on a common carrier. These items are not distribited to the general market and are often special order.

I also have an 11-23 on a standard crank. I like this for flatter rides, but this cassette will not do well on hilly rides. Do you use the 11 cog much? If you don't, consider a 12-27. These can be found at affordable prices.

I would recommend getting a new cassette. They're designed to shift better with the specific choice of cog sizes and properly shaped teeth. Note that changing from 23 to 25 is less than a 10% change - if you want to really feel a big difference in the gearing you may want to make a more substantial change.
As Grumpy indicated, you should check your chain first to be sure it isn't worn. Putting a new cassette on with a worn chain will generally work fine, but it'll start wearing out the cassette prematurely. And you might well need a longer chain anyway - that just depends on how much extra length your current chain may have. You want to be sure that the chain will be able to go on the large/large combination without binding - even if you never plan to use that gear combination it's a good idea to check that it'll work since you might sometime inadvertently try to shift into it and cause damage if the chain is too short.

You need a new cassette. Looking at gear-inch numbers won't tell you anything more than a simple comparsion of 23/25 = .92. That means that you get 8% lower gearing with a 25T large cog.

As for the chain length, that's been asked and answered nearly every day on this forum and the answer is always the same - 2T more gear requires only 1/2 inch more chain, but the minimum increment of change is 1 inch. Whether the chain needs to be any longer depends on how the length was determined and your chainstay length. If someone set the length by the big/big plus 1 inch method and there is no excess length, then you'll need another inch. If the little/little method was used and done properly, the chain will be long enough. You can usually tell just by how extended the RD cage is, when it's shifted to the big/big combo (with the old cassette). If the cage has a fair amount of forward travel left, it will probably work. Mount the new cassette and slowly shift into the largest cog. If the chain is eally too short, it shouldn't even shift into the largest cog, or the chain might start to jam-up. Just don't do this test out on the road, under a load and you'll be fine.

https://www.parktool.com/blog/repair-...-length-sizing

To answer your questions..

*You would need to add to your chain a little.
*Don't bother trying to change cogs. Just buy a cassette.
*Your short cage derailleur will work fine.

Personally i like a 12/26 cassette. It's low enough that i can climb anything with ease but i can still keep up with other riders without using my big chainring.

When cassettes were first introduced, I thought part of their benefit was the ability to mix and match gears as you pleased. Seems not to be the case, especially as some of the sprockets are actually clustered together.