Upgrading a crank set I presently have a 3x7 speed crankset with a sealed cartridge bottom bracket on my touring bike and want to upgrade to a new Hollowtech II bottom bracket and crankset, specifically, the SHIMANO Claris 3x8-Speed Road Bicycle Crankset (FC-R2030). My shifters are 3x7 speed indexed, and I will stay with the 7 speed rear cassette. Is there any reason why the 3x8 front crankset would not work?
A 3x8 crank will work with a 7 speed system. 7 and 8 speed chains are the same, as is the spacing between the chainrings.

The Claris crank specification can be found on the Shimano Manuals and Technical Documents site   here. The FC-R2030 seems to only come in 50-39-30. If that is larger than you current crank you'll need to check that you have sufficient clearance with the drive side chainstay. 

The specification says the FC-R2030 works with either a 68 or 73mm bottom bracket shell, so that will work whatever your bike has. Note it also says what bottom bracket you need (BB-RS500) that will fit either shell width. 

The FC-R2030 provides a chainline of 45mm - that's the standard for road triples. You'll definitely want to check that that is what you bike runs as there's a chance it runs the mountain bike triple standard 47.5mm. Measure from the center of the seat tube to the middle ring. More info here https://www.sheldonbrown.com/chainline.html.

If you have 47.5mm chainline you'll need to look at a mountain triple crank instead of a road triple crank.