At the beginning of "Yesterday Once More," the only instrumentation to accompany Carpenter's voice is piano. During the first half of the second verse, there's a bit of bass, but it's in a higher register so it's not as noticeable. After the line "How I wondered where they'd gone" (where "they" refers to the "happy times" from the previous line), the bass drops to a lower register, becoming more prominent, and organ and drums come in. It's a musical representation of the next line: "But they're back again."
The first verse links the joy of those "happy times" with music:
When I was young, I'd listen to the radioSo when more instruments come in to represent being "back again," it's almost literal. The music of those "happy times" - which the additional instrumentation represents - has actually come "back again."
Waitin' for my favorite songs
When they played, I'd sing along
It made me smile