The excerpt is in C clef the entire time.
If you look at the beginning - the beginning of the variation (which is treated notationally like a new piece) you'll see an F Clef followed by a reduced-size C clef.
This publisher/editor/engraver chose to engrave the music this way. Today we would more frequently just put the Tenor clef at the beginning so it looks like it does on the 2nd page. Ordinarily, the previous page would have had a "cautionary" clef prior to the last bar.
But since this is a variation form, it might look kind of silly to have a clef change at the end of the variation (and since this excerpt doesn't go to the end of Variation 7, we can't see how it was handled at the end).
So instead, they put it at the beginning - it was bass clef, now it's Tenor.
Since this is a "solo" - an excerpt of a longer piece, it's likely the bass was in F clef until this part came up.
I'm honestly not sure of the practice for variation forms like this because I've never looked that closely at them. A Schirmer edition of Mozart Piano Sonatas I have puts a double bar at the end of each variation (if not a repeat) and treats each variation of a new piece. I found one where it does exactly this - the Treble and Bass start the piece, but the lower staff has a small-sized Treble clef immediately preceding the first note. So I would bet it was common practice in this situation. A quick scan through the book for other Theme and Variations movements (I'm not going to spend all day on this!) found another - interestingly where the first I talked about each new variation was indented, in the second they weren't. It's highly likely these two pieces were originally engraved at different times and the plates were used again later for the book - and it's also likely that some pages had to be re-engraved to make them fit and so on. But the second piece also doesn't start any variations with a new clef that doesn't allow for it to be placed later into the piece.
On any of the page turns - where the leftmost bar is not the beginning of a variation, the regular full-sized Tenor clef is used and that's standard practice.
Why it's in Tenor clef the whole time - it's high enough in the bass's range that it would have been many ledger lines in the bass clef. Tenor clef makes more sense - keeps the notes on the staff (and again, common practice for bass and cello players).