If your existing setup is, as an example, a 42/26 and 11-34 (just made up numbers) then your existing max tooth count is 76t, and minimum is 37t. The chain must be long enough to accommodate up to 76 teeth, plus chainstay length and derailleur S-takeup length. That same chain must be short enough to not cause derailleur cage overlap in the 37t setting of 26/11.
Let's say your new setup is 42/26 and 11-30. Now the maximum you must accommodate is a 72t configuration. The minimum is unchanged.
But I'll bet dollars to doughnuts that your 11-34 cassette has a cog somewhere around 30t. Maybe it's 29, or 31, but close to 30. There's no reason to think that because you went to a smaller cassette where the maximum rear cog is the same size as your
#3 cog used to be would require changing the chain size.
"
Require", I say... your drivetrain performance will be no worse using the same chain length. However, running a longer than necessary chain length is not
optimal. Given that you are going to a smaller cassette, you can get away now with optimizing your chain length in a way that could possibly improve drivetrain performance more than was possible with the old cassette and its longer-chain requirement. In theory you could reduce the chain by four links (two outer, two inner) and possibly improve performance slightly because there will be less slack for the derailleur to take up. The smaller cassette enables you to run a chain length that is less demanding on the derailleur's capacity.
Now if your minimum setting changed too; lets say you went to a 10t smallest rear cog... in that case it may be
necessary to remove a link to eliminate derailleur cage overlap in the small/small setting. Or if you went to a 36t rear cassette, it may be necessary to add two links if your chain was already as short as possible before going to a larger cassette.
It's also worth mentioning that if your chain has more than a thousand miles on it, cassette swap time is chain replacement time too. True, chains last a lot longer than 1000 miles if properly cared for. But a brand new cassette is less prone to early wear when it's not mated to a chain that has any degree of stretch (wear). My suggestion is this: Buy your new chain. Then resize your old one and ride around a bit to test the size. If it is too short or too long, it's better to discover this with the chain you're about to throw away than with the new one.