Can I replace chainrings without replacing the rest of the drive train?
The simple answer is yes, you can just change the crankset without replacing the entire drive train however there are other considerations. Depends on if your changing rings out or replacing the set and cranks. Other considerations if doing a full replacement are:

Chain line

When selecting a new crank set you need to ensure it aligns with the current chainline of your bike. If you change the chain line you may not be able to use all of the gears on your rear cassette in all gears up front.

Bottom bracket

You need to ensure that a new crankset will be compatible with your current BB spindle length and interface. (square, octo, isis, hollowtech etc.) If your BB has a lot of wear once you have the cranks off its not a bad idea to change the BB at the same time as they're not that big a cost. Also it's sometimes if you get a good deal on a crankset to get a matching BB as they're the cheaper item.

Chain length

You may need to shorten the chain going to smaller rings if the derailleur doesn't  provide enough tension.

Rear derailleur capacity

Not a problem when shifting to a smaller crankset but if going larger you would need to ensure that the rear derailleur would handle the additional cogs. There are tools online to help calculate this.

Wear

If the chain and rear cassette are showing signs of wear it's often wise to replace these at the same time as they will wear a new crankset faster.

Chain width

If you are buying a new crankset it has to be appropriate for the number of gears on your bike, this is because chains are different widths to accommodate more gears on the rear cassette. The rest of the drive train is sized to fit the chain width.