Cheers up, with Republican around, becoming valued (5)
I believe the answer is:
rated
'valued' is the definition.
(rating is a kind of valuing)
'cheers up with republican around' is the wordplay.
'cheers' becomes 'ta' (both can mean thank you).
'up' is a reversal indicator (in down clue: letters go upwards).
'with' says to put letters next to each other.
'republican' becomes 'R' (political abbreviation).
'around' becomes 'ed' (I can't explain this - if you can you should give a lot more credence to this answer).
'ta' back-to-front is 'at'.
'at' put after 'r' is 'rat'.
'rat'+'ed'='RATED'
'becoming' acts as a link.
Can you help me to learn more?
(Other definitions for rated that I've seen before include "Scolded (archaic); assessed" , "Admired" , "deserved" , "Highly valued" , "Castigated" .)