What kind of yeast?
There are three kinds of yeast used by most home bakers. One, "compressed yeast," needs to be stored in the refrigerator. This type ages and loses its potency very quickly no matter how well stored. For this and a couple of other reasons, it's not very popular anymore.
The two which are most commonly found in the supermarket are "active dry yeast," and another which goes under the two names of instant yeast, and "bread machine yeast."
If you've got "active dry yeast" sold in envelopes -- you can increase its shelf life slightly by storing closed envelopes in the refrigerator. However, once an envelope is opened it's not worth trying to preserve the remaineder. Active dry yeast is the type of yeast which must be "proofed," in warm water before mixing into dough.
If you've got "bread machine yeast," which is usually sold in a jar, you certainly can increase its useful life by tightly closing the lid and refrigerating. It will retain its potency for months.
If you've got "instant yeast," which is often sold vacuum packed, wrapped in foil, in small commercial amounts (SAF, Fermipan, Eagle, etc), empty the contents into an airtight container and store in the refrigerator for up to several months.
These three different types came about through different technologies used to keep a high proportion of yeast spores healthy while inactive. I think you can guess that bread machine yeast and instant yeast come from the same background. However bread machine was further developed, marketed and packaged for home bakers, while instant was developed for commercial bakers. Over the past few years manufacturers have been putting straight instant yeast in bread machine packaging, and have introduced instant yeast packaged in envelopes for the home baker into the supermarket.
Bread machine yeast used to have, and sometimes but not always still has one or two ingredients to prevent clumping and keep it easy to mix. However, instant yeast is so well granualized, those turn out to be unnecessary. Bread machine yeast tends to be held for a longer time by the manufacturer and retailers, so is less reliable than the instant yeast sold in small commercial quantities. It's also considerably more expensive. Instant yeast is your best bet for nearly all yeast applications.