Packed theirs in the one that’s going up (2,3,4)

'going up' is the definition.
I know nothing about this answer so I can't tell whether this works.

'packed theirs in the one' is the wordplay.
I cannot really understand how this works, but
an anagram of 'theirs' is 'theris' which is located in the answer.
'one' could be 'o' (I've seen this in other clues) and 'o' is found in the answer.
The remaining letters 'ne' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'that's' acts as a link.

Can you help me to learn more?