One climbing the walls is up, not bad and constant, say (5)
I believe the answer is:
gecko
'one climbing the walls' is the definition.
'up not bad and constant say' is the wordplay.
'up' is a reversal indicator (in down clue: letters go upwards).
'not bad' becomes 'ok'.
'and' says to put letters next to each other.
'constant' becomes 'c' (mathematical abbreviation).
'say' becomes 'eg'.
'ok'+'c'+'eg'='okceg'
'okceg' reversed gives 'GECKO'.
'is' acts as a link.
(Other definitions for gecko that I've seen before include "Cold-blooded type" , "Small lizard with adhesive foot-pads" , "Malaysian climber" , "one climbing the walls?" , "Reptile" .)