Top copper sees support for uniform going up more sharply (7)

I believe the answer is:
steeper
'support for uniform going up more sharply' is the definition.
I can't tell whether this defines the answer.
'top copper' is the wordplay.
I cannot really see how this works, but
'top' could be 'tee' (T-shirt) and 'tee' is located in the answer.
'copper' could be 'p' and 'p' is found in the answer.
The remaining letters 'ser' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
'sees' acts as a link.
Can you help me to learn more?
(Other definitions for steeper that I've seen before include "greater inclination" , "More inclined" , "More precipitous" .)
