A king on way up to be an emperor (4)
I believe the answer is:
tsar
'emperor' is the definition.
(I've seen this before)
'a king on way up' is the wordplay.
'king' becomes 'r' (r is abbreviation for rex).
'on' means one lot of letters go next to another.
'way' becomes 'st' (**).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'a' after 'r' is 'ra'.
'ra'+'st'='rast'
'rast' in reverse letter order is 'TSAR'.
'to be an' acts as a link.
(Other definitions for tsar that I've seen before include "Supreme authority" , "Potentate" , "Title given to the kings of Bulgaria" , "Autocrat" , "Rats to the Russian emperor" .)